graphical representation of statistical data in economics

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How to Construct and Interpret Graphs

Learning objectives.

• Understand how graphs show the relationship between two or more variables and explain how a graph elucidates the nature of the relationship.
• Define the slope of a curve.
• Distinguish between a movement along a curve, a shift in a curve, and a rotation in a curve.

Much of the analysis in economics deals with relationships between variables. A variable is simply a quantity whose value can change. A graph is a pictorial representation of the relationship between two or more variables. The key to understanding graphs is knowing the rules that apply to their construction and interpretation. This section defines those rules and explains how to draw a graph.

Drawing a Graph

To see how a graph is constructed from numerical data, we will consider a hypothetical example. Suppose a college campus has a ski club that organizes day-long bus trips to a ski area about 100 miles from the campus. The club leases the bus and charges $10 per passenger for a round trip to the ski area. In addition to the revenue the club collects from passengers, it also receives a grant of $200 from the school’s student government for each day the bus trip is available. The club thus would receive $200 even if no passengers wanted to ride on a particular day.

The table in Figure 21.1 “Ski Club Revenues” shows the relationship between two variables: the number of students who ride the bus on a particular day and the revenue the club receives from a trip. In the table, each combination is assigned a letter (A, B, etc.); we will use these letters when we transfer the information from the table to a graph.

Figure 21.1 Ski Club Revenues

The ski club receives $10 from each passenger riding its bus for a trip to and from the ski area plus a payment of $200 from the student government for each day the bus is available for these trips. The club’s revenues from any single day thus equal $200 plus $10 times the number of passengers. The table relates various combinations of the number of passengers and club revenues.

We can illustrate the relationship shown in the table with a graph. The procedure for showing the relationship between two variables, like the ones in Figure 21.1 “Ski Club Revenues” , on a graph is illustrated in Figure 21.2 “Plotting a Graph” . Let us look at the steps involved.

Figure 21.2 Plotting a Graph

Here we see how to show the information given in Figure 21.1 “Ski Club Revenues” in a graph.

Step 1. Draw and Label the Axes

The two variables shown in the table are the number of passengers taking the bus on a particular day and the club’s revenue from that trip. We begin our graph in Panel (a) of Figure 21.2 “Plotting a Graph” by drawing two axes to form a right angle. Each axis will represent a variable. The axes should be carefully labeled to reflect what is being measured on each axis.

It is customary to place the independent variable on the horizontal axis and the dependent variable on the vertical axis. Recall that, when two variables are related, the dependent variable is the one that changes in response to changes in the independent variable. Passengers generate revenue, so we can consider the number of passengers as the independent variable and the club’s revenue as the dependent variable. The number of passengers thus goes on the horizontal axis; the club’s revenue from a trip goes on the vertical axis. In some cases, the variables in a graph cannot be considered independent or dependent. In those cases, the variables may be placed on either axis; we will encounter such a case in the chapter that introduces the production possibilities model. In other cases, economists simply ignore the rule; we will encounter that case in the chapter that introduces the model of demand and supply. The rule that the independent variable goes on the horizontal axis and the dependent variable goes on the vertical usually holds, but not always.

The point at which the axes intersect is called the origin of the graph. Notice that in Figure 21.2 “Plotting a Graph” the origin has a value of zero for each variable.

In drawing a graph showing numeric values, we also need to put numbers on the axes. For the axes in Panel (a), we have chosen numbers that correspond to the values in the table. The number of passengers ranges up to 40 for a trip; club revenues from a trip range from $200 (the payment the club receives from student government) to $600. We have extended the vertical axis to $800 to allow some changes we will consider below. We have chosen intervals of 10 passengers on the horizontal axis and $100 on the vertical axis. The choice of particular intervals is mainly a matter of convenience in drawing and reading the graph; we have chosen the ones here because they correspond to the intervals given in the table.

We have drawn vertical lines from each of the values on the horizontal axis and horizontal lines from each of the values on the vertical axis. These lines, called gridlines, will help us in Step 2.

Step 2. Plot the Points

Each of the rows in the table in Figure 21.1 “Ski Club Revenues” gives a combination of the number of passengers on the bus and club revenue from a particular trip. We can plot these values in our graph.

We begin with the first row, A, corresponding to zero passengers and club revenue of $200, the payment from student government. We read up from zero passengers on the horizontal axis to $200 on the vertical axis and mark point A. This point shows that zero passengers result in club revenues of $200.

The second combination, B, tells us that if 10 passengers ride the bus, the club receives $300 in revenue from the trip—$100 from the $10-per-passenger charge plus the $200 from student government. We start at 10 passengers on the horizontal axis and follow the gridline up. When we travel up in a graph, we are traveling with respect to values on the vertical axis. We travel up by $300 and mark point B.

Points in a graph have a special significance. They relate the values of the variables on the two axes to each other. Reading to the left from point B, we see that it shows $300 in club revenue. Reading down from point B, we see that it shows 10 passengers. Those values are, of course, the values given for combination B in the table.

We repeat this process to obtain points C, D, and E. Check to be sure that you see that each point corresponds to the values of the two variables given in the corresponding row of the table.

The graph in Panel (b) is called a scatter diagram. A scatter diagram shows individual points relating values of the variable on one axis to values of the variable on the other.

Step 3. Draw the Curve

The final step is to draw the curve that shows the relationship between the number of passengers who ride the bus and the club’s revenues from the trip. The term “curve” is used for any line in a graph that shows a relationship between two variables.

We draw a line that passes through points A through E. Our curve shows club revenues; we shall call it R 1 . Notice that R 1 is an upward-sloping straight line. Notice also that R 1 intersects the vertical axis at $200 (point A). The point at which a curve intersects an axis is called the intercept of the curve. We often refer to the vertical or horizontal intercept of a curve; such intercepts can play a special role in economic analysis. The vertical intercept in this case shows the revenue the club would receive on a day it offered the trip and no one rode the bus.

To check your understanding of these steps, we recommend that you try plotting the points and drawing R 1 for yourself in Panel (a). Better yet, draw the axes for yourself on a sheet of graph paper and plot the curve.

The Slope of a Curve

In this section, we will see how to compute the slope of a curve. The slopes of curves tell an important story: they show the rate at which one variable changes with respect to another.

The slope of a curve equals the ratio of the change in the value of the variable on the vertical axis to the change in the value of the variable on the horizontal axis, measured between two points on the curve. You may have heard this called “the rise over the run.” In equation form, we can write the definition of the slope as

Equation 21.1

Equation 21.1 is the first equation in this text. Figure 21.3 “Reading and Using Equations” provides a short review of working with equations. The material in this text relies much more heavily on graphs than on equations, but we will use equations from time to time. It is important that you understand how to use them.

Figure 21.3 Reading and Using Equations

Many equations in economics begin in the form of Equation 21.1 , with the statement that one thing (in this case the slope) equals another (the vertical change divided by the horizontal change). In this example, the equation is written in words. Sometimes we use symbols in place of words. The basic idea though, is always the same: the term represented on the left side of the equals sign equals the term on the right side. In Equation 21.1 there are three variables: the slope, the vertical change, and the horizontal change. If we know the values of two of the three, we can compute the third. In the computation of slopes that follow, for example, we will use values for the two variables on the right side of the equation to compute the slope.

Figure 21.4 “Computing the Slope of a Curve” shows R 1 and the computation of its slope between points B and D. Point B corresponds to 10 passengers on the bus; point D corresponds to 30. The change in the horizontal axis when we go from B to D thus equals 20 passengers. Point B corresponds to club revenues of $300; point D corresponds to club revenues of $500. The change in the vertical axis equals $200. The slope thus equals $200/20 passengers, or $10/passenger.

Figure 21.4 Computing the Slope of a Curve

• Select two points; we have selected points B and D.
• The slope equals the vertical change divided by the horizontal change between the two points.
• Between points B and D, the slope equals $200/20 passengers = $10/passenger.
• The slope of this curve is the price per passenger. The fact that it is positive suggests a positive relationship between revenue per trip and the number of passengers riding the bus. Because the slope of this curve is $10/passenger between any two points on the curve, the relationship between club revenue per trip and the number of passengers is linear.

We have applied the definition of the slope of a curve to compute the slope of R 1 between points B and D. That same definition is given in Equation 21.1 . Applying the equation, we have:

The slope of this curve tells us the amount by which revenues rise with an increase in the number of passengers. It should come as no surprise that this amount equals the price per passenger. Adding a passenger adds $10 to the club’s revenues.

Notice that we can compute the slope of R 1 between any two points on the curve and get the same value; the slope is constant. Consider, for example, points A and E. The vertical change between these points is $400 (we go from revenues of $200 at A to revenues of $600 at E). The horizontal change is 40 passengers (from zero passengers at A to 40 at E). The slope between A and E thus equals $400/(40 passengers) = $10/passenger . We get the same slope regardless of which pair of points we pick on R 1 to compute the slope. The slope of R 1 can be considered a constant, which suggests that it is a straight line. When the curve showing the relationship between two variables has a constant slope, we say there is a linear relationship between the variables. A linear curve is a curve with constant slope.

The fact that the slope of our curve equals $10/passenger tells us something else about the curve—$10/passenger is a positive, not a negative, value. A curve whose slope is positive is upward sloping. As we travel up and to the right along R 1 , we travel in the direction of increasing values for both variables. A positive relationship between two variables is one in which both variables move in the same direction. Positive relationships are sometimes called direct relationships. There is a positive relationship between club revenues and passengers on the bus. We will look at a graph showing a negative relationship between two variables in the next section.

A Graph Showing a Negative Relationship

A negative relationship is one in which two variables move in opposite directions. A negative relationship is sometimes called an inverse relationship. The slope of a curve describing a negative relationship is always negative. A curve with a negative slope is always downward sloping.

As an example of a graph of a negative relationship, let us look at the impact of the cancellation of games by the National Basketball Association during the 1998–1999 labor dispute on the earnings of one player: Shaquille O’Neal. During the 1998–1999 season, O’Neal was the center for the Los Angeles Lakers.

O’Neal’s salary with the Lakers in 1998–1999 would have been about $17,220,000 had the 82 scheduled games of the regular season been played. But a contract dispute between owners and players resulted in the cancellation of 32 games. Mr. O’Neal’s salary worked out to roughly $210,000 per game, so the labor dispute cost him well over $6 million. Presumably, he was able to eke out a living on his lower income, but the cancellation of games cost him a great deal.

We show the relationship between the number of games canceled and O’Neal’s 1998–1999 basketball earnings graphically in Figure 21.5 “Canceling Games and Reducing Shaquille O’Neal’s Earnings” . Canceling games reduced his earnings, so the number of games canceled is the independent variable and goes on the horizontal axis. O’Neal’s earnings are the dependent variable and go on the vertical axis. The graph assumes that his earnings would have been $17,220,000 had no games been canceled (point A, the vertical intercept). Assuming that his earnings fell by $210,000 per game canceled, his earnings for the season were reduced to $10,500,000 by the cancellation of 32 games (point B). We can draw a line between these two points to show the relationship between games canceled and O’Neal’s 1998–1999 earnings from basketball. In this graph, we have inserted a break in the vertical axis near the origin. This allows us to expand the scale of the axis over the range from $10,000,000 to $18,000,000. It also prevents a large blank space between the origin and an income of $10,500,000—there are no values below this amount.

Figure 21.5 Canceling Games and Reducing Shaquille O’Neal’s Earnings

If no games had been canceled during the 1998–1999 basketball season, Shaquille O’Neal would have earned $17,220,000 (point A). Assuming that his salary for the season fell by $210,000 for each game canceled, the cancellation of 32 games during the dispute between NBA players and owners reduced O’Neal’s earnings to $10,500,000 (point B).

What is the slope of the curve in Figure 21.5 “Canceling Games and Reducing Shaquille O’Neal’s Earnings” ? We have data for two points, A and B. At A, O’Neal’s basketball salary would have been $17,220,000. At B, it is $10,500,000. The vertical change between points A and B equals -$6,720,000. The change in the horizontal axis is from zero games canceled at A to 32 games canceled at B. The slope is thus

Notice that this time the slope is negative, hence the downward-sloping curve. As we travel down and to the right along the curve, the number of games canceled rises and O’Neal’s salary falls. In this case, the slope tells us the rate at which O’Neal lost income as games were canceled.

The slope of O’Neal’s salary curve is also constant. That means there was a linear relationship between games canceled and his 1998–1999 basketball earnings.

Shifting a Curve

When we draw a graph showing the relationship between two variables, we make an important assumption. We assume that all other variables that might affect the relationship between the variables in our graph are unchanged. When one of those other variables changes, the relationship changes, and the curve showing that relationship shifts.

Consider, for example, the ski club that sponsors bus trips to the ski area. The graph we drew in Figure 21.2 “Plotting a Graph” shows the relationship between club revenues from a particular trip and the number of passengers on that trip, assuming that all other variables that might affect club revenues are unchanged. Let us change one. Suppose the school’s student government increases the payment it makes to the club to $400 for each day the trip is available. The payment was $200 when we drew the original graph. Panel (a) of Figure 21.6 “Shifting a Curve: An Increase in Revenues” shows how the increase in the payment affects the table we had in Figure 21.1 “Ski Club Revenues” ; Panel (b) shows how the curve shifts. Each of the new observations in the table has been labeled with a prime: A′, B′, etc. The curve R 1 shifts upward by $200 as a result of the increased payment. A shift in a curve implies new values of one variable at each value of the other variable. The new curve is labeled R 2 . With 10 passengers, for example, the club’s revenue was $300 at point B on R 1 . With the increased payment from the student government, its revenue with 10 passengers rises to $500 at point B′ on R 2 . We have a shift in the curve.

Figure 21.6 Shifting a Curve: An Increase in Revenues

The table in Panel (a) shows the new level of revenues the ski club receives with varying numbers of passengers as a result of the increased payment from student government. The new curve is shown in dark purple in Panel (b). The old curve is shown in light purple.

It is important to distinguish between shifts in curves and movements along curves. A movement along a curve is a change from one point on the curve to another that occurs when the dependent variable changes in response to a change in the independent variable. If, for example, the student government is paying the club $400 each day it makes the ski bus available and 20 passengers ride the bus, the club is operating at point C′ on R 2 . If the number of passengers increases to 30, the club will be at point D′ on the curve. This is a movement along a curve; the curve itself does not shift.

Now suppose that, instead of increasing its payment, the student government eliminates its payments to the ski club for bus trips. The club’s only revenue from a trip now comes from its $10/passenger charge. We have again changed one of the variables we were holding unchanged, so we get another shift in our revenue curve. The table in Panel (a) of Figure 21.7 “Shifting a Curve: A Reduction in Revenues” shows how the reduction in the student government’s payment affects club revenues. The new values are shown as combinations A″ through E″ on the new curve, R 3 , in Panel (b). Once again we have a shift in a curve, this time from R 1 to R 3 .

Figure 21.7 Shifting a Curve: A Reduction in Revenues

The table in Panel (a) shows the impact on ski club revenues of an elimination of support from the student government for ski bus trips. The club’s only revenue now comes from the $10 it charges to each passenger. The new combinations are shown as A″ – E″. In Panel (b) we see that the original curve relating club revenue to the number of passengers has shifted down.

The shifts in Figure 21.6 “Shifting a Curve: An Increase in Revenues” and Figure 21.7 “Shifting a Curve: A Reduction in Revenues” left the slopes of the revenue curves unchanged. That is because the slope in all these cases equals the price per ticket, and the ticket price remains unchanged. Next, we shall see how the slope of a curve changes when we rotate it about a single point.

Rotating a Curve

A rotation of a curve occurs when we change its slope, with one point on the curve fixed. Suppose, for example, the ski club changes the price of its bus rides to the ski area to $30 per trip, and the payment from the student government remains $200 for each day the trip is available. This means the club’s revenues will remain $200 if it has no passengers on a particular trip. Revenue will, however, be different when the club has passengers. Because the slope of our revenue curve equals the price per ticket, the slope of the revenue curve changes.

Panel (a) of Figure 21.8 “Rotating a Curve” shows what happens to the original revenue curve, R 1 , when the price per ticket is raised. Point A does not change; the club’s revenue with zero passengers is unchanged. But with 10 passengers, the club’s revenue would rise from $300 (point B on R 1 ) to $500 (point B′ on R 4 ). With 20 passengers, the club’s revenue will now equal $800 (point C′ on R 4 ).

Figure 21.8 Rotating a Curve

A curve is said to rotate when a single point remains fixed while other points on the curve move; a rotation always changes the slope of a curve. Here an increase in the price per passenger to $30 would rotate the revenue curve from R 1 to R 4 in Panel (a). The slope of R 4 is $30 per passenger.

The new revenue curve R 4 is steeper than the original curve. Panel (b) shows the computation of the slope of the new curve between points B′ and C′. The slope increases to $30 per passenger—the new price of a ticket. The greater the slope of a positively sloped curve, the steeper it will be.

We have now seen how to draw a graph of a curve, how to compute its slope, and how to shift and rotate a curve. We have examined both positive and negative relationships. Our work so far has been with linear relationships. Next we will turn to nonlinear ones.

Key Takeaways

• A graph shows a relationship between two or more variables.
• An upward-sloping curve suggests a positive relationship between two variables. A downward-sloping curve suggests a negative relationship between two variables.
• The slope of a curve is the ratio of the vertical change to the horizontal change between two points on the curve. A curve whose slope is constant suggests a linear relationship between two variables.
• A change from one point on the curve to another produces a movement along the curve in the graph. A shift in the curve implies new values of one variable at each value of the other variable. A rotation in the curve implies that one point remains fixed while the slope of the curve changes.

The following table shows the relationship between the number of gallons of gasoline people in a community are willing and able to buy per week and the price per gallon. Plot these points in the grid provided and label each point with the letter associated with the combination. Notice that there are breaks in both the vertical and horizontal axes of the grid. Draw a line through the points you have plotted. Does your graph suggest a positive or a negative relationship? What is the slope between A and B? Between B and C? Between A and C? Is the relationship linear?

Now suppose you are given the following information about the relationship between price per gallon and the number of gallons per week gas stations in the community are willing to sell.

Plot these points in the grid provided and draw a curve through the points you have drawn. Does your graph suggest a positive or a negative relationship? What is the slope between D and E? Between E and F? Between D and F? Is this relationship linear?

Answer to Try It!

Here is the first graph. The curve’s downward slope tells us there is a negative relationship between price and the quantity of gasoline people are willing and able to buy. This curve, by the way, is a demand curve (the next one is a supply curve). We will study demand and supply soon; you will be using these curves a great deal. The slope between A and B is −0.002 (slope = vertical change/horizontal change = −0.20/100). The slope between B and C and between A and C is the same. That tells us the curve is linear, which, of course, we can see—it is a straight line.

Here is the supply curve. Its upward slope tells us there is a positive relationship between price per gallon and the number of gallons per week gas stations are willing to sell. The slope between D and E is 0.002 (slope equals vertical change/horizontal change = 0.20/100). Because the curve is linear, the slope is the same between any two points, for example, between E and F and between D and F.

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Graphical Re­presentation of Statistical Data

Let us make an in-depth study of the graphical representation of statistical data.

Introduction:

Besides textual and tabular presentations of statistical data, the third and perhaps the most attractive and commonly used popular modem device to exhibit any data in a systematic manner is to represent them with suitable and appropriate diagrams and pictures.

The usual and effective means in this context are: graphs, charts, pictures, etc. and they are really and surely capable of depicting some important features of the data which they individually are not able to exhibit. Selection of the appropriate diagram actually depends on the nature of the raw data available and the purpose or the area in which it will be applied. However, only certain limited information can be supplied through a particular diagram and as such each diagram has certain specific limitations of its own.

A few commonly used diagrams applied on different occasions in various disciplines today are the line diagram, bar diagram, ogive, pie dia­gram and the pictogram (as prescribed in the syllabus).

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It may be noted that diagrammatic represen­tations of statistical information is appealing to the eyes. Hidden facts may also be detected once such information are presented graphically. Further, graphs of statistical data clearly bring out the relative importance of different figures, the trend or tendency of the values of the variables involved can be studied too.

Line Diagrams :

This kind of a diagram becomes suitable for representing data supplied chronologically in an ascending or descending order. Usually, it shows the behaviour of a variable over time. Successive values of a variable at different periods or places are plotted as separate points on a two dimensional plane and the locus of all those points joined together form a continuous line segment, called line diagram.

While tracing out such a diagram, the usual convention is to show the successive values of the variable under study along the vertical axis in an increasing order and the time dimension along the horizontal axis. It should carefully be noted that none of the two axes be too long or too short with respect to each other.

This is very much necessary mainly to avoid unpredictable and wide fluctuations in the given values of the variable. The origin or the (0, 0) point at the left hand comer should clearly be mentioned so as to discard wrong impression on the process of drawing.

Two or more (but finite number of) line segments can also be drawn on the same quadrant when information on different variables over the same period or time are simultaneously represented using the same unit of measurement along the same axis. We can thus draw a number of line- diagrams for different data series on the same quadrant.

They can distinctly and attractively be displayed on a screen for presentation with various colourful lines. When the values of the variable under consideration change at a constant rate over the same successive time intervals, the diagram will take the shape of a straight line. Other-wise, it will represent various concave, convex or irregular curves when viewed from the origin.

Let us now represent a common line diagram below:

Line diagrams showing total values of Exports and Imports during 1987-96 have been presented in Fig. 7.1. This figure has been drawn on the basis of data shown in Table 7.4.

Two separate line diagrams showing fluctua­tions in the values of exports and imports of India during (1987—96) are shown below:

In the diagram drawn above the successive years from the table are shown horizontally and the corresponding values of export and import are shown vertically and the points are located separately on the plane from the middle of the respective years and the lacus of those points exhibit the trend along the line diagrams.

Bar Diagrams :

It is another well-known useful statistical weapon to represent raw data decently. This device is applied specially in a situation where the given data can be classified on the basis of a non- measurable criterion e.g., standards of college education in different states of India at the present time.

This is very often called cross-section data. More precisely, a bar graph is formed as a collection of rectangles having the same width or breadth placed successively at equal distance. Practically, the height of each bar placed vertically represents the value of the variable on the identical class interval shown horizontally.

Usually, these bars are placed either vertically on the horizontal axis or horizontally on the vertical axis and they are thus known as vertical bar chart or horizontal bar chart. Conventionally vertical bar charts are formed with the time series data.

Actually speaking, no formal rule as to how much space to be given in between the two bars is there. If necessary, no space in between two bars can be given. In some other cases, suitable and reasonable gaps in-between two bars may also be allowed.

Let us imprint simple and suitable examples of bar diagrams be­low:

(a) Simple Vertical Bar Diagram:

Volume of population in a number of states in India in 2001 is given below—represents the data with the aid of vertical bars.

Fig. 7.2 Shows population of a number of 5 States in India in a particular year (2001):

(b) Horizontal Bar Diagram:

Volume of production and profit of five different organisations operating under a particular industry with separate productive capacities are given below for the two successive years 2011 and 2012.

We represent the information through an ideal bar diagram. Here Fig. 7.3 is drawn below on the basis of Table 7.6. We have chosen this horizontal bar diagram to facilitate comparison of perfor­mances of 5 organisations for the years 2011 and 2012, respectively.

Horizontal bars show production (in thousands) and profit (Rs. thousand) of five organisations of India in the financial year 2011-12.

(c) Multiple or Component Bar Diagram

These diagrams are used in a situation where two or more related categories are to be compared simultaneously.

Consider the following example:

Labour employment and their percentages in 2000 and 2010 in a factory is given below. Repre­sent them in terms of multiple or component bar diagrams.

Component bar diagrams show number of labourers of different categories and their respec­tive percentages for the years 2000 and 2010.

Pie Diagram :

It is another effective statistical device to represent quantitative data obtainable on many occasions simply and diagrammatically. When the various parts of the values of a variable possesses different properties then to express the inherent relationship among them and also with the aggregate value of the variable, pie diagram possibly is the best device.

Here, the aggregate value of the variable is expressed as the total area of a circle with a reasonable radius. The entire area in the circle is subdivided into a number of parts by several radii which are separately related to the total area of the circle and also maintain the same proportional relation with the angle at the centre.

For drawing it correctly, we convert the particular given values of the variable as a percen­tage of the total value of the variable. As the angle at the centre is 360°, it is supposed to express 100 p.c. value of the variable where 1 p.c. value of the variable is equivalent to an angle of 3.6° at the centre.

We can thus easily convert the individual given values of the variable into the required angles at the centre. Then we draw a complete circle taking any standard radius and put the angles found from the numerical exercise separately at the centre. Each separate part in the circle signifies a particular section of the data. Let us represent a simple pie diagram below constructed with the usual method prescribed and followed for its computation by converting the following information into that diagram.

Expenditure incurred by the Planning Commission of India on Education in the last 5-year economic plan.

Table 7.8(A): Educational Expenditure in the Last Five-year Economic Plan:

Let us first convert the given data into respective percentages and then into the required angles to be shown at the centre in two more co­lumns and represent them in the following way:

Here, angle at the Centre = Percentage x 3.6.

Pie diagram drawn below on the basis of Table 7.8 (B) shows expenditure on education at various stages in the last 5-year economic plan.

Ogive or Cumulative Frequency Polygon:

An ogive is another statistical tool primarily used for finding out different quartiles in a distribution. From such a device we can also identify the number of observations lying above or below a certain value of the concerned variable.

This kind of a diagram is drawn for a fre­quency distribution of a continuous variable in terms of cumulative frequencies of both the types (more than or less than type). While drawing this diagram we consider the given values of the variable horizontally and the corresponding cumulative frequencies (of either type) vertically.

Cumulative frequency of less than type is zero for the lowest given value of the variable and similarly cumulative frequency of greater than type is zero for the highest value of the variable considered. Using the data available from a production organisation, Ogives of both the types are drawn below for our ready reference.

Ogives (of both the types) drawn on the basis of the above data and determination of the median wage:

Here, being the middle-most value of the given wage rates, the median wage is found OB (= Rs. 52) because only at this wage rate the two cumulative frequency curves intersect at point A representing two cumulative frequencies (less-than and greater-than) of both the types exactly equal (AB = 25) with each other. Hence, the median wage is OB = Rs. 52.00.

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Module 1: Economic Thinking

Introduction to graphs in economics, what you’ll learn to do: use graphs in common economic applications.

In this course, the most common way you will encounter economic models is in graphical form.

A graph is a visual representation of numerical information. Graphs condense detailed numerical information to make it easier to see patterns (such as “trends”) among data. For example, which countries have larger or smaller populations? A careful reader could examine a long list of numbers representing the populations of many countries, but with more than two hundred nations in the world, searching through such a list would take concentration and time. Putting these same numbers on a graph, listing them from highest to lowest, would reveal population patterns much more readily.

Economists use graphs not only as a compact and readable presentation of data, but also for visually representing relationships and connections—in other words, they function as models. As such, they can be used to answer questions. For example: How do increasing interest rates affect home sales? Graphing the results can help illuminate the answers.

This section provides an overview of graphing—just to make sure you’re up to speed on the basics. It’s important to feel comfortable with the way graphs work before using them to understand new concepts.

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Graphical Representation of Data

Graphical representation of data is an attractive method of showcasing numerical data that help in analyzing and representing quantitative data visually. A graph is a kind of a chart where data are plotted as variables across the coordinate. It became easy to analyze the extent of change of one variable based on the change of other variables. Graphical representation of data is done through different mediums such as lines, plots, diagrams, etc. Let us learn more about this interesting concept of graphical representation of data, the different types, and solve a few examples.

Definition of Graphical Representation of Data

A graphical representation is a visual representation of data statistics-based results using graphs, plots, and charts. This kind of representation is more effective in understanding and comparing data than seen in a tabular form. Graphical representation helps to qualify, sort, and present data in a method that is simple to understand for a larger audience. Graphs enable in studying the cause and effect relationship between two variables through both time series and frequency distribution. The data that is obtained from different surveying is infused into a graphical representation by the use of some symbols, such as lines on a line graph, bars on a bar chart, or slices of a pie chart. This visual representation helps in clarity, comparison, and understanding of numerical data.

Representation of Data

The word data is from the Latin word Datum, which means something given. The numerical figures collected through a survey are called data and can be represented in two forms - tabular form and visual form through graphs. Once the data is collected through constant observations, it is arranged, summarized, and classified to finally represented in the form of a graph. There are two kinds of data - quantitative and qualitative. Quantitative data is more structured, continuous, and discrete with statistical data whereas qualitative is unstructured where the data cannot be analyzed.

Principles of Graphical Representation of Data

The principles of graphical representation are algebraic. In a graph, there are two lines known as Axis or Coordinate axis. These are the X-axis and Y-axis. The horizontal axis is the X-axis and the vertical axis is the Y-axis. They are perpendicular to each other and intersect at O or point of Origin. On the right side of the Origin, the Xaxis has a positive value and on the left side, it has a negative value. In the same way, the upper side of the Origin Y-axis has a positive value where the down one is with a negative value. When -axis and y-axis intersect each other at the origin it divides the plane into four parts which are called Quadrant I, Quadrant II, Quadrant III, Quadrant IV. This form of representation is seen in a frequency distribution that is represented in four methods, namely Histogram, Smoothed frequency graph, Pie diagram or Pie chart, Cumulative or ogive frequency graph, and Frequency Polygon.

Advantages and Disadvantages of Graphical Representation of Data

Listed below are some advantages and disadvantages of using a graphical representation of data:

• It improves the way of analyzing and learning as the graphical representation makes the data easy to understand.
• It can be used in almost all fields from mathematics to physics to psychology and so on.
• It is easy to understand for its visual impacts.
• It shows the whole and huge data in an instance.
• It is mainly used in statistics to determine the mean, median, and mode for different data

The main disadvantage of graphical representation of data is that it takes a lot of effort as well as resources to find the most appropriate data and then represent it graphically.

Rules of Graphical Representation of Data

While presenting data graphically, there are certain rules that need to be followed. They are listed below:

• Suitable Title: The title of the graph should be appropriate that indicate the subject of the presentation.
• Measurement Unit: The measurement unit in the graph should be mentioned.
• Proper Scale: A proper scale needs to be chosen to represent the data accurately.
• Index: For better understanding, index the appropriate colors, shades, lines, designs in the graphs.
• Data Sources: Data should be included wherever it is necessary at the bottom of the graph.
• Simple: The construction of a graph should be easily understood.
• Neat: The graph should be visually neat in terms of size and font to read the data accurately.

Uses of Graphical Representation of Data

The main use of a graphical representation of data is understanding and identifying the trends and patterns of the data. It helps in analyzing large quantities, comparing two or more data, making predictions, and building a firm decision. The visual display of data also helps in avoiding confusion and overlapping of any information. Graphs like line graphs and bar graphs, display two or more data clearly for easy comparison. This is important in communicating our findings to others and our understanding and analysis of the data.

Types of Graphical Representation of Data

Data is represented in different types of graphs such as plots, pies, diagrams, etc. They are as follows,

Related Topics

Listed below are a few interesting topics that are related to the graphical representation of data, take a look.

• x and y graph
• Frequency Polygon
• Cumulative Frequency

Examples on Graphical Representation of Data

Example 1 : A pie chart is divided into 3 parts with the angles measuring as 2x, 8x, and 10x respectively. Find the value of x in degrees.

We know, the sum of all angles in a pie chart would give 360º as result. ⇒ 2x + 8x + 10x = 360º ⇒ 20 x = 360º ⇒ x = 360º/20 ⇒ x = 18º Therefore, the value of x is 18º.

Example 2: Ben is trying to read the plot given below. His teacher has given him stem and leaf plot worksheets. Can you help him answer the questions? i) What is the mode of the plot? ii) What is the mean of the plot? iii) Find the range.

Solution: i) Mode is the number that appears often in the data. Leaf 4 occurs twice on the plot against stem 5.

Hence, mode = 54

ii) The sum of all data values is 12 + 14 + 21 + 25 + 28 + 32 + 34 + 36 + 50 + 53 + 54 + 54 + 62 + 65 + 67 + 83 + 88 + 89 + 91 = 958

To find the mean, we have to divide the sum by the total number of values.

Mean = Sum of all data values ÷ 19 = 958 ÷ 19 = 50.42

iii) Range = the highest value - the lowest value = 91 - 12 = 79

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Practice Questions on Graphical Representation of Data

Faqs on graphical representation of data, what is graphical representation.

Graphical representation is a form of visually displaying data through various methods like graphs, diagrams, charts, and plots. It helps in sorting, visualizing, and presenting data in a clear manner through different types of graphs. Statistics mainly use graphical representation to show data.

What are the Different Types of Graphical Representation?

The different types of graphical representation of data are:

• Stem and leaf plot
• Scatter diagrams
• Frequency Distribution

Is the Graphical Representation of Numerical Data?

Yes, these graphical representations are numerical data that has been accumulated through various surveys and observations. The method of presenting these numerical data is called a chart. There are different kinds of charts such as a pie chart, bar graph, line graph, etc, that help in clearly showcasing the data.

What is the Use of Graphical Representation of Data?

Graphical representation of data is useful in clarifying, interpreting, and analyzing data plotting points and drawing line segments , surfaces, and other geometric forms or symbols.

What are the Ways to Represent Data?

Tables, charts, and graphs are all ways of representing data, and they can be used for two broad purposes. The first is to support the collection, organization, and analysis of data as part of the process of a scientific study.

What is the Objective of Graphical Representation of Data?

The main objective of representing data graphically is to display information visually that helps in understanding the information efficiently, clearly, and accurately. This is important to communicate the findings as well as analyze the data.

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1.11: Introduction to Graphs in Economics

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What you’ll learn to do: use graphs in common economic applications

In this course, the most common way you will encounter economic models is in graphical form.

A graph is a visual representation of numerical information. Graphs condense detailed numerical information to make it easier to see patterns (such as “trends”) among data. For example, which countries have larger or smaller populations? A careful reader could examine a long list of numbers representing the populations of many countries, but with more than two hundred nations in the world, searching through such a list would take concentration and time. Putting these same numbers on a graph, listing them from highest to lowest, would reveal population patterns much more readily.

Economists use graphs not only as a compact and readable presentation of data, but also for visually representing relationships and connections—in other words, they function as models. As such, they can be used to answer questions. For example: How do increasing interest rates affect home sales? Graphing the results can help illuminate the answers.

This section provides an overview of graphing—just to make sure you’re up to speed on the basics. It’s important to feel comfortable with the way graphs work before using them to understand new concepts.

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An alternative graphical modeling for economics: Econographicology

• Published: 04 November 2015
• Volume 51 , pages 2115–2139, ( 2017 )

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• Mario Arturo Ruiz Estrada 1  

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The rationale of Econographicology revolves around the efficacy of multidimensional graphs as the most effective visual tool to understand any economic phenomenon from a multidimensional view. The main motivation behind the creation of Econographicology is to evaluate multidimensional graphs evolved so far in economics and to develop new type of multidimensional graphs to facilitate the study of economics, as well as finance and business. Thereby, the mission of Econographicology is to offer academics, researchers and policy maker’s an alternative multidimensional graphical modeling approach for the research and teaching–learning process of economics, finance and business from a multidimensional perspective. Hence, this alternative multidimensional graphical modeling approach is offer a set of multi-dimensional coordinate spaces to build different types of multidimensional graphs to study any economic phenomenon. The following new types of multi-dimensional coordinate spaces are presented: the 5-dimensional coordinate space (vertical position and horizontal position), the mega-dynamic disks coordinate space (vertical position and horizontal position), and the mega-disks networks mapping.

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Faculty of Economics and Administration (FEA), University of Malaya (UM), 50603, Kuala Lumpur, Malaysia

Mario Arturo Ruiz Estrada

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American Economic Review; Canadian Journal of Economics; Econometrica; Economica; Economic History Review; Economic Journal; International Economic Review; Journal of Economic History; Journal of Economic Literature; Journal of Political Economy; Oxford Economic Papers; Quarterly Journal of Economics; Review of Economic Studies; Review of Economics and Statistics; Canadian Journal of Economics and Political Science; Journal of Economic Abstracts; Contributions to Canadian Economics; Journal of Labor Economics; Journal of Applied Econometrics; Journal of Economic Perspectives; Publications of the American Economic Association; Brookings Papers on Economic Activity. Microeconomics and American Economic Association Quarterly.

A List of publications are using Econographicology successfully (SciencesDirect.com 2014 ):

Ruiz Estrada, M.A. 2004. “Trade Liberalization Evaluation (TLE) Methodology.” Journal of Policy Modeling, 26(8–9): 903–1104.

Ruiz Estrada, M.A. and Su Fei Yap (2006). “Openness Growth Monitoring (OGM) Model.” Journal of Policy Modeling, 28(3): 235–346.

Ruiz Estrada, M.A. and Park, D. 2008. “Korean Unification: How Painful and How Costly?” Journal of Policy Modeling, 30(1): 87–100.

Ruiz Estrada, M.A. 2008. “Demand & Supply Surfaces.” Malaysian Journal of Economic Studies, 45(2): 71–77.

Ruiz Estrada, M.A. 2009. “GDP-Surface.” International Journal of Economic Research, 6(2): 279–291.

Ruiz Estrada, M.A. 2010. “The Visualization of Complex Economic Phenomena from a Multi-Dimensional Graphical Perspective: The U.S. Economy (1929-2008) Case Study.” International Journal of Economic Research, 7(2): 271–276.

Ruiz Estrada, M.A. 2011.”Policy Modeling: Definition, Classification and Evaluation.” Journal of Policy Modeling, 33(3): 523–536.

Ruiz Estrada, M.A. 2011. “Multi-Dimensional Coordinate Spaces.” International Journal Physical Studies, 6(3): 340–357.

Ruiz Estrada, M.A. 2012. “A new Multidimensional Graphical Approach for Mathematics and Physics.” Malaysian Journal of Sciences, 31(2): 175–198.

Ruiz Estrada, M.A. and Yap, S.F. 2013. “The Origins and Evolution of Policy Modeling.” Journal of Policy Modeling, 35 (1): 170–182.

Ruiz Estrada, M.A. 2013. “Is It Possible to Apply Multidimensional Graphical Methods in the Teaching and Learning of Economics?” Contemporary Economics, 7(4):123–138.

Ruiz Estrada, M.A. 2013. “Alternative Multidimensional Economic Theoretical Frameworks for Microeconomics and Macroeconomics.” International Journal of Economic Research, 10(2): 327–346.

Ruiz Estrada, M.A., Yap, S.F. and Park, D. 2013. “The Natural Disaster Vulnerability Evaluation Model (NDVE-Model): An Application to the Northeast Japan Earthquake and Tsunami of March 2011.” Disasters Journal, 38(s2): s206–s229.

Ruiz Estrada, M.A. and Park, D. 2013.”China’s Unification: Myth or Reality?” Panoeconomicus, 61(4):441–469.

Ruiz Estrada, M.A. 2014. “The Economics Waves Effect of the U.S. Economy on the World Economy.” Contemporary Economics, 8(3): 247.

Ruiz Estrada, M.A. and Ndoma, A. 2014. “How Crime Affects Economic Performance: the Case of Guatemala.” Journal of Policy Modeling, 36(5): 867-882.

Ruiz Estrada, M.A. Tahir, M. and Chandran, VRG. Tahir, M. 2015. “An Introduction to the Multidimensional Real Time Economic Modeling.” Contemporary Economics.

Ruiz Estrada, M.A., Park, D., Kim, G., Khan, Q. 2015. “The Economic Impact of Terrorism: A New Model and Its Application to Pakistan.” Journal of Policy Modeling (JPM).

Saavedra-Rivano, N. and Ruiz Estrada, M.A. 2015. “An Alternative Free Trade Agreement Scheme for Developing Countries: The Micro-Free Trade Territory (MFTT).” Quality and Quantity.

Ruiz Estrada, M.A. Park, D. and Kim, G. 2015. “An Economic Model of the Wartime Economy: An Application to a Possible Sino-Japanese Conflict.” FUDAN Journal of Humanities and Social Sciences.

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Ruiz Estrada, M.A. An alternative graphical modeling for economics: Econographicology. Qual Quant 51 , 2115–2139 (2017). https://doi.org/10.1007/s11135-015-0280-3

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Learning Objectives

By the end of this chapter, the student should be able to:

• Display data graphically and interpret graphs: stemplots, bar charts, frequency polygons, histograms, etc.

Once you have collected data, what will you do with it? Data can be described and presented in many different formats. For example, suppose you want to find a change in temperature in a particular city over time. Looking at all the raw data can be confusing and overwhelming. A better way to look at that data would be to create a graph that displays the data in a visual manner. Then patterns can more easily be discerned.

In this chapter, you will study graphical ways to describe and display your data. You will learn to create, and more importantly, interpret a variety of graph types, and you will learn when to use each type of graph.

A statistical graph is a tool that helps you learn about the shape or distribution of a sample or a population. A graph can be a more effective way of presenting data than a mass of numbers because we can see where data clusters and where there are only a few data values. Newspapers and the Internet use graphs to show trends and to enable readers to compare facts and figures quickly. Statisticians often graph data first to get a picture of the data. Then, more formal tools may be applied.

Some of the types of graphs that are used to summarize and organize data are the dot plot, the bar graph, the histogram, the stem-and-leaf plot, the frequency polygon (a type of broken line graph), the pie chart, and the box plot. In this chapter, we will briefly look at stem-and-leaf plots, line graphs, and bar graphs, as well as frequency polygons, and time series graphs.

This book contains instructions for constructing some graph types using Excel.

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Graphical Representation of Data: In today’s world of the internet and connectivity, there is a lot of data available, and some or other method is needed for looking at large data, the patterns, and trends in it. There is an entire branch in mathematics dedicated to dealing with collecting, analyzing, interpreting, and presenting numerical data in visual form in such a way that it becomes easy to understand and the data becomes easy to compare as well, the branch is known as Statistics .

The branch is widely spread and has a plethora of real-life applications such as Business Analytics, demography, Astro statistics, and so on. In this article, we have provided everything about the graphical representation of data, including its types, rules, advantages, etc.

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• What is Graphical Representation?

Types of Graphical Representations

Graphical representations used in maths, principles of graphical representations, advantages and disadvantages of using graphical system, general rules for graphical representation of data, solved examples on graphical representation of data, what is graphical representation.

Graphics Representation is a way of representing any data in picturized form. It helps a reader to understand the large set of data very easily as it gives us various data patterns in visualized form.

There are two ways of representing data,

• Pictorial Representation through graphs.

They say, “A picture is worth a thousand words”.  It’s always better to represent data in a graphical format. Even in Practical Evidence and Surveys, scientists have found that the restoration and understanding of any information is better when it is available in the form of visuals as Human beings process data better in visual form than any other form.

Does it increase the ability 2 times or 3 times? The answer is it increases the Power of understanding 60,000 times for a normal Human being, the fact is amusing and true at the same time.

Comparison between different items is best shown with graphs, it becomes easier to compare the crux of the data about different items. Let’s look at all the different types of graphical representations briefly: 

Line Graphs

A line graph is used to show how the value of a particular variable changes with time. We plot this graph by connecting the points at different values of the variable. It can be useful for analyzing the trends in the data and predicting further trends. 

A bar graph is a type of graphical representation of the data in which bars of uniform width are drawn with equal spacing between them on one axis (x-axis usually), depicting the variable. The values of the variables are represented by the height of the bars. 

Histograms 

This is similar to bar graphs, but it is based frequency of numerical values rather than their actual values. The data is organized into intervals and the bars represent the frequency of the values in that range. That is, it counts how many values of the data lie in a particular range. 

It is a plot that displays data as points and checkmarks above a number line, showing the frequency of the point. 

Stem and Leaf Plot 

This is a type of plot in which each value is split into a “leaf”(in most cases, it is the last digit) and “stem”(the other remaining digits). For example: the number 42 is split into leaf (2) and stem (4).  

Box and Whisker Plot 

These plots divide the data into four parts to show their summary. They are more concerned about the spread, average, and median of the data. 

It is a type of graph which represents the data in form of a circular graph. The circle is divided such that each portion represents a proportion of the whole. 

Graphs in Math are used to study the relationships between two or more variables that are changing. Statistical data can be summarized in a better way using graphs. There are basically two lines of thoughts of making graphs in maths: 

• Value-Based or Time Series Graphs

Frequency Based

Value-based or time series graphs .

These graphs allow us to study the change of a variable with respect to another variable within a given interval of time. The variables can be anything. Time Series graphs study the change of variable with time. They study the trends, periodic behavior, and patterns in the series. We are more concerned with the values of the variables here rather than the frequency of those values. 

Example: Line Graph

These kinds of graphs are more concerned with the distribution of data. How many values lie between a particular range of the variables, and which range has the maximum frequency of the values. They are used to judge a spread and average and sometimes median of a variable under study. 

Example: Frequency Polygon, Histograms.

All types of graphical representations require some rule/principles which are to be followed. These are some algebraic principles. When we plot a graph, there is an origin, and we have our two axes. These two axes divide the plane into four parts called quadrants. The horizontal one is usually called the x-axis and the other one is called the y-axis. The origin is the point where these two axes intersect.

The thing we need to keep in mind about the values of the variable on the x-axis is that positive values need to be on the right side of the origin and negative values should be on the left side of the origin. Similarly, for the variable on the y-axis, we need to make sure that the positive values of this variable should be above the x-axis and negative values of this variable must be below the y-axis. 

• It gives us a summary of the data which is easier to look at and analyze.
• It saves time.
• We can compare and study more than one variable at a time.

Disadvantages

It usually takes only one aspect of the data and ignores the other. For example, A bar graph does not represent the mean, median, and other statistics of the data. 

We should keep in mind some things while plotting and designing these graphs. The goal should be a better and clear picture of the data. Following things should be kept in mind while plotting the above graphs: 

• Whenever possible, the data source must be mentioned for the viewer.
• Always choose the proper colors and font sizes. They should be chosen to keep in mind that the graphs should look neat.
• The measurement Unit should be mentioned in the top right corner of the graph.
• The proper scale should be chosen while making the graph, it should be chosen such that the graph looks accurate.
• Last but not the least, a suitable title should be chosen.

Frequency Polygon

A frequency polygon is a graph that is constructed by joining the midpoint of the intervals. The height of the interval or the bin represents the frequency of the values that lie in that interval. 

• Diagrammatic and Graphic Presentation of Data
• What are the different ways of Data Representation?

Question 1: What are different types of frequency-based plots? 

Types of frequency based plots:  Histogram Frequency Polygon Box Plots

Question 2: A company with an advertising budget of Rs 10,00,00,000 has planned the following expenditure in the different advertising channels such as TV Advertisement, Radio, Facebook, Instagram, and Printed media. The table represents the money spent on different channels. 

Draw a bar graph for the following data. 

• Put each of the channels on the x-axis
• The height of the bars is decided by the value of each channel.

Question 3: Draw a line plot for the following data 

• Put each of the x-axis row value on the x-axis
• joint the value corresponding to the each value of the x-axis.

Question 4: Make a frequency plot of the following data: 

• Draw the class intervals on the x-axis and frequencies on the y-axis.
• Calculate the mid point of each class interval.

Now join the mid points of the intervals and their corresponding frequencies on the graph. 

This graph shows both the histogram and frequency polygon for the given distribution.

Graphical Representation of Data – FAQs

What are the advantages of using graphs to represent data.

Graphs offer visualization, clarity, and easy comparison of data, aiding in outlier identification and predictive analysis.

What are the common types of graphs used for data representation?

Common graph types include bar, line, pie, histogram, and scatter plots, each suited for different data representations and analysis purposes.

How do you choose the most appropriate type of graph for your data?

Select a graph type based on data type, analysis objective, and audience familiarity to effectively convey information and insights.

How do you create effective labels and titles for graphs?

Use descriptive titles, clear axis labels with units, and legends to ensure the graph communicates information clearly and concisely.

How do you interpret graphs to extract meaningful insights from data?

Interpret graphs by examining trends, identifying outliers, comparing data across categories, and considering the broader context to draw meaningful insights and conclusions.

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Historical Development of the Graphical Representation of Statistical Data

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J. M. Keynes, Historical Development of the Graphical Representation of Statistical Data, The Economic Journal , Volume 48, Issue 190, 1 June 1938, Pages 281–282, https://doi.org/10.2307/2224943

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