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This pdf includes the following topics:-

Meaning of Graphic Representation of Data

General Principles of Graphic Representation

Methods to Represent a Frequency Distribution

Pie Graph Formula

Advantages of a Pie Graph

Meaning of Graphic Representation of Data

General Principles of Graphic Representation

Methods to Represent a Frequency Distribution

Pie Graph Formula

Advantages of a Pie Graph

1.
Graphical Representation of Data

Meaning, Principles and Methods

Meaning of Graphic Representation of Data:

Graphic representation is another way of analysing numerical data. A graph is a sort of Graph

through which statistical data are represented in the form of lines or curves drawn across the

coordinated points plotted on its surface.

Graphs enable us in studying the cause and effect relationship between two variables. Graphs

help to measure the extent of change in one variable when another variable changes by a

certain amount.

Graphs also enable us in studying both time series and frequency distribution as they give clear

account and precise picture of problem. Graphs are also easy to understand and eye catching.

General Principles of Graphic Representation:

There are some algebraic principles which apply to all types of graphic representation of data. In

a graph there are two lines called coordinate axes. One is vertical known as Y axis and the

other is horizontal called X axis. These two lines are perpendicular to each other. Where these

two lines intersect each other is called ‘0’ or the Origin. On the X axis the distances right to the

origin have positive value (see fig. 7.1) and distances left to the origin have negative value. On

the Y axis distances above the origin have a positive value and below the origin have a negative

Methods to Represent a Frequency Distribution:

Generally four methods are used to represent a frequency distribution graphically. These are

Histogram, Smoothed frequency graph and Ogive or Cumulative frequency graph and pie

Kinds Graphical Representation:-

1. Pie Graph

2. Bar graph

3. Histogram

4. Frequency Polygon

5. Cumulative Frequency Curve

6. Cumulative Percentage Curve

1. Pie Graph

A pie Graph is a type of graph that represents the data in the circular graph. A pie Graph

requires a list of categorical variables and the numerical variables. Here, the term “pie”

represents the whole and the “slices” represents the parts of the whole. In this article, we will

discuss the definition of a pie Graph, its formula, an example to create a pie Graph, uses,

advantages and disadvantages in detail.

What is Pie Graph?

Meaning, Principles and Methods

Meaning of Graphic Representation of Data:

Graphic representation is another way of analysing numerical data. A graph is a sort of Graph

through which statistical data are represented in the form of lines or curves drawn across the

coordinated points plotted on its surface.

Graphs enable us in studying the cause and effect relationship between two variables. Graphs

help to measure the extent of change in one variable when another variable changes by a

certain amount.

Graphs also enable us in studying both time series and frequency distribution as they give clear

account and precise picture of problem. Graphs are also easy to understand and eye catching.

General Principles of Graphic Representation:

There are some algebraic principles which apply to all types of graphic representation of data. In

a graph there are two lines called coordinate axes. One is vertical known as Y axis and the

other is horizontal called X axis. These two lines are perpendicular to each other. Where these

two lines intersect each other is called ‘0’ or the Origin. On the X axis the distances right to the

origin have positive value (see fig. 7.1) and distances left to the origin have negative value. On

the Y axis distances above the origin have a positive value and below the origin have a negative

Methods to Represent a Frequency Distribution:

Generally four methods are used to represent a frequency distribution graphically. These are

Histogram, Smoothed frequency graph and Ogive or Cumulative frequency graph and pie

Kinds Graphical Representation:-

1. Pie Graph

2. Bar graph

3. Histogram

4. Frequency Polygon

5. Cumulative Frequency Curve

6. Cumulative Percentage Curve

1. Pie Graph

A pie Graph is a type of graph that represents the data in the circular graph. A pie Graph

requires a list of categorical variables and the numerical variables. Here, the term “pie”

represents the whole and the “slices” represents the parts of the whole. In this article, we will

discuss the definition of a pie Graph, its formula, an example to create a pie Graph, uses,

advantages and disadvantages in detail.

What is Pie Graph?

2.
The “pie Graph” also is known as “circle Graph” divides the circular statistical graphic into

sectors or slices in order to illustrate the numerical problems. Each sector denotes a

proportionate part of the whole. To find out the composition of something, Pie-Graph works the

best at that time. In most of the cases, pie Graphs replace some other graphs like the bar graph,

line plots, histograms etc.

Pie Graph Formula

The pie Graph is an important type of data representation. It contains different segments and

sectors in which each segment and sectors of a pie Graph forms a certain portion of the

total(percentage). The total of all the data is equal to 360°.

The total value of the pie is always 100%.

To work out with the percentage for a pie Graph, follow the steps given below:

Categorize the data

Calculate the total

Divide the categories

Convert into percentages

Finally, calculate the degrees

Therefore, the pie Graph formula is given as

(Given Data/Total value of Data) × 360°

Example :-

Imagine a teacher surveys her class on the basis of their favourite Sports:

Football Hockey Cricket Basketball Badminton

10 5 5 10 10

The data above can be represented by a pie-Graph as following and by using the circle graph

formula i.e. the pie Graph formula given below. It makes the size of portion easy to understand.

Step 1: First, Enter the data into the table.

Football Hockey Cricket Basketball Badminton

10 5 5 10 10

Step 2: Add all the values in the table to get the total.

Total students are 40 in this case.

Step 3: Next, divide each value by the total and multiply by 100 to get a per cent:

Football Hockey Cricket Basketball Badminton

sectors or slices in order to illustrate the numerical problems. Each sector denotes a

proportionate part of the whole. To find out the composition of something, Pie-Graph works the

best at that time. In most of the cases, pie Graphs replace some other graphs like the bar graph,

line plots, histograms etc.

Pie Graph Formula

The pie Graph is an important type of data representation. It contains different segments and

sectors in which each segment and sectors of a pie Graph forms a certain portion of the

total(percentage). The total of all the data is equal to 360°.

The total value of the pie is always 100%.

To work out with the percentage for a pie Graph, follow the steps given below:

Categorize the data

Calculate the total

Divide the categories

Convert into percentages

Finally, calculate the degrees

Therefore, the pie Graph formula is given as

(Given Data/Total value of Data) × 360°

Example :-

Imagine a teacher surveys her class on the basis of their favourite Sports:

Football Hockey Cricket Basketball Badminton

10 5 5 10 10

The data above can be represented by a pie-Graph as following and by using the circle graph

formula i.e. the pie Graph formula given below. It makes the size of portion easy to understand.

Step 1: First, Enter the data into the table.

Football Hockey Cricket Basketball Badminton

10 5 5 10 10

Step 2: Add all the values in the table to get the total.

Total students are 40 in this case.

Step 3: Next, divide each value by the total and multiply by 100 to get a per cent:

Football Hockey Cricket Basketball Badminton

3.
(10/40) × 100 (5/ 40) × 100 (5/40) ×100 (10/ 40) ×100 (10/40)× 100

=25% =12.5% =12.5% =25% =25%

Step 4: Next to know how many degrees for each “pie sector” we need, we will take a full circle

of 360° and follow the calculations below:

The central angle of each component = (Value of each component/sum of values of all the

components) ✕360°

Football Hockey Cricket Basketball Badminton

(10/ 40)× 360° (5 / 40) × 360° (5/40) × 360° (10/ 40)× 360° (10/ 40) × 360°

=90° =45° =45° =90° =90°

Now you can draw a pie Graph.

Step 5: Draw a circle and use the protractor to measure the degree of each sector.

Uses of Pie Graph

1. Pie diagram is useful when one wants to picture proportions of the total in a striking way.

2. When a population is stratified and each strata is to be presented as a percentage at that

time pie diagram is used.

Advantages of a Pie Graph

The picture is simple and easy-to-understand

Data can be represented visually as a fractional part of a whole

It helps in providing an effective communication tool for the even uninformed audience

=25% =12.5% =12.5% =25% =25%

Step 4: Next to know how many degrees for each “pie sector” we need, we will take a full circle

of 360° and follow the calculations below:

The central angle of each component = (Value of each component/sum of values of all the

components) ✕360°

Football Hockey Cricket Basketball Badminton

(10/ 40)× 360° (5 / 40) × 360° (5/40) × 360° (10/ 40)× 360° (10/ 40) × 360°

=90° =45° =45° =90° =90°

Now you can draw a pie Graph.

Step 5: Draw a circle and use the protractor to measure the degree of each sector.

Uses of Pie Graph

1. Pie diagram is useful when one wants to picture proportions of the total in a striking way.

2. When a population is stratified and each strata is to be presented as a percentage at that

time pie diagram is used.

Advantages of a Pie Graph

The picture is simple and easy-to-understand

Data can be represented visually as a fractional part of a whole

It helps in providing an effective communication tool for the even uninformed audience

4.
Provides a data comparison for the audience at a glance to give an immediate analysis or

to quickly understand information

No need for readers to examine or measure underlying numbers themselves which can

be removed by using this Graph

To emphasize a few points you want to make, you can manipulate pieces of data in the

pie Graph

Disadvantages of a Pie Graph

It becomes less effective, If there are too many pieces of data to use

If there are too many pieces of data, and even if you add data labels and numbers may

not help here, they themselves may become crowded and hard to read

As this Graph only represents one data set, You need a series to compare multiple sets

This may make it more difficult for readers when it comes to analyze and assimilate

2. Bar Diagram

Also known as a column graph, a bar graph or a bar diagram is a pictorial representation

of data. It is shown in the form of rectangles spaced out with equal spaces between them

and having equal width. The equal width and equal space criteria are important

characteristics of a bar graph.

Note that the height (or length) of each bar corresponds to the frequency of a particular

observation. You can draw bar graphs both, vertically or horizontally depending on whether

you take the frequency along the vertical or horizontal axes respectively. Let us take an

example to understand how a bar graph is drawn.

Example:-Construct a Bar Graph from following data.

Students No. of Students

Basketball 15

Volleyball 25

Football 10

Total = 50

Toabove table depicts the number of students of a class engaged in any one of the three sports

given.Note that the number of students is actually the frequency. So, if we take frequency to be

represented on the y-axis and the sports on the x-axis, taking each unit on the y-axis to be equal to

5 students, we would get a graph that resembles the one below.

The blue rectangles here are called bars. Note that the bars have equal width and are equally

spaced, as mentioned above. This is a simple bar diagram.

to quickly understand information

No need for readers to examine or measure underlying numbers themselves which can

be removed by using this Graph

To emphasize a few points you want to make, you can manipulate pieces of data in the

pie Graph

Disadvantages of a Pie Graph

It becomes less effective, If there are too many pieces of data to use

If there are too many pieces of data, and even if you add data labels and numbers may

not help here, they themselves may become crowded and hard to read

As this Graph only represents one data set, You need a series to compare multiple sets

This may make it more difficult for readers when it comes to analyze and assimilate

2. Bar Diagram

Also known as a column graph, a bar graph or a bar diagram is a pictorial representation

of data. It is shown in the form of rectangles spaced out with equal spaces between them

and having equal width. The equal width and equal space criteria are important

characteristics of a bar graph.

Note that the height (or length) of each bar corresponds to the frequency of a particular

observation. You can draw bar graphs both, vertically or horizontally depending on whether

you take the frequency along the vertical or horizontal axes respectively. Let us take an

example to understand how a bar graph is drawn.

Example:-Construct a Bar Graph from following data.

Students No. of Students

Basketball 15

Volleyball 25

Football 10

Total = 50

Toabove table depicts the number of students of a class engaged in any one of the three sports

given.Note that the number of students is actually the frequency. So, if we take frequency to be

represented on the y-axis and the sports on the x-axis, taking each unit on the y-axis to be equal to

5 students, we would get a graph that resembles the one below.

The blue rectangles here are called bars. Note that the bars have equal width and are equally

spaced, as mentioned above. This is a simple bar diagram.

5.
Histogram is a non-cumulative frequency graph, it is drawn on a natural scale in which the

representative frequencies of the different class of values are represented through vertical

rectangles drawn closed to each other. Measure of central tendency, mode can be easily

determined with the help of this graph.

How to draw a Histogram:

1. Represent the class intervals of the variables along the X axis and their frequencies along the Y-

axis on natural scale.

2. Start X axis with the lower limit of the lowest class interval. When the lower limit happens to be a

distant score from the origin give a break in the X-axis n to indicate that the vertical axis has been

moved in for convenience.

3. Now draw rectangular bars in parallel to Y axis above each of the class intervals with class units

as base: The areas of rectangles must be proportional to the frequencies of the cor¬responding

Example :- Construct a Histogram Graph from following data.

C.I f

20-24 2

25-29 2

30-34 5

35-39 10

40-44 6

45-49 2

50-54 3

representative frequencies of the different class of values are represented through vertical

rectangles drawn closed to each other. Measure of central tendency, mode can be easily

determined with the help of this graph.

How to draw a Histogram:

1. Represent the class intervals of the variables along the X axis and their frequencies along the Y-

axis on natural scale.

2. Start X axis with the lower limit of the lowest class interval. When the lower limit happens to be a

distant score from the origin give a break in the X-axis n to indicate that the vertical axis has been

moved in for convenience.

3. Now draw rectangular bars in parallel to Y axis above each of the class intervals with class units

as base: The areas of rectangles must be proportional to the frequencies of the cor¬responding

Example :- Construct a Histogram Graph from following data.

C.I f

20-24 2

25-29 2

30-34 5

35-39 10

40-44 6

45-49 2

50-54 3

6.
In this graph we shall take class intervals in the X axis and frequencies in the Y

axis. Before plotting the graph we have to convert the class into their exact limits.

Advantages of histogram:

1. It is easy to draw and simple to understand.

2. It helps us to understand the distribution easily and quickly.

3. It is more precise than the polygene.

Limitations of histogram:

1. It is not possible to plot more than one distribution on same axes as histogram.

2. Comparison of more than one frequency distribution on the same axes is not

axis. Before plotting the graph we have to convert the class into their exact limits.

Advantages of histogram:

1. It is easy to draw and simple to understand.

2. It helps us to understand the distribution easily and quickly.

3. It is more precise than the polygene.

Limitations of histogram:

1. It is not possible to plot more than one distribution on same axes as histogram.

2. Comparison of more than one frequency distribution on the same axes is not

7.
3. It is not possible to make it smooth.

Uses of histogram:

1. Represents the data in graphic form.

2. Provides the knowledge of how the scores in the group are distributed. Whether

the scores are piled up at the lower or higher end of the distribution or are evenly

and regularly distributed throughout the scale.

3. Frequency Polygon. The frequency polygon is a frequency graph which is drawn

by joining the coordinating points of the mid-values of the class intervals and their

corresponding frequencies.

4.Frequency Polygon

1. Draw a horizontal line at the bottom of graph paper named ‘X’ axis. Mark off the

exact limits of the class intervals along this axis. It is better to start with c.i. of lowest

value. When the lowest score in the distribution is a large number we cannot show it

graphically if we start with the origin. Therefore put a break in the X axis () to

indicate that the vertical axis has been moved in for convenience. Two additional

points may be added to the two extreme ends.

2. Draw a vertical line through the extreme end of the horizontal axis known as OY

axis. Along this line mark off the units to represent the frequencies of the class

intervals. The scale should be chosen in such a way that it will make the largest

frequency (height) of the polygon approximately 75 percent of the width of the

3. Plot the points at a height proportional to the frequencies directly above the point

on the horizontal axis representing the mid-point of each class interval.

4. After plotting all the points on the graph join these points by a series of short

straight lines to form the frequency polygon. In order to complete the figure two

additional intervals at the high end and low end of the distribution should be

included. The frequency of these two intervals will be zero.

Draw a frequency polygon from the following data:

Uses of histogram:

1. Represents the data in graphic form.

2. Provides the knowledge of how the scores in the group are distributed. Whether

the scores are piled up at the lower or higher end of the distribution or are evenly

and regularly distributed throughout the scale.

3. Frequency Polygon. The frequency polygon is a frequency graph which is drawn

by joining the coordinating points of the mid-values of the class intervals and their

corresponding frequencies.

4.Frequency Polygon

1. Draw a horizontal line at the bottom of graph paper named ‘X’ axis. Mark off the

exact limits of the class intervals along this axis. It is better to start with c.i. of lowest

value. When the lowest score in the distribution is a large number we cannot show it

graphically if we start with the origin. Therefore put a break in the X axis () to

indicate that the vertical axis has been moved in for convenience. Two additional

points may be added to the two extreme ends.

2. Draw a vertical line through the extreme end of the horizontal axis known as OY

axis. Along this line mark off the units to represent the frequencies of the class

intervals. The scale should be chosen in such a way that it will make the largest

frequency (height) of the polygon approximately 75 percent of the width of the

3. Plot the points at a height proportional to the frequencies directly above the point

on the horizontal axis representing the mid-point of each class interval.

4. After plotting all the points on the graph join these points by a series of short

straight lines to form the frequency polygon. In order to complete the figure two

additional intervals at the high end and low end of the distribution should be

included. The frequency of these two intervals will be zero.

Draw a frequency polygon from the following data:

8.
In this graph we shall take the class intervals (marks in mathematics) in X axis, and frequencies

(Number of students) in the Y axis. Before plotting the graph we have to convert the c.i. into

their exact limits and extend one c.i. in each end with a frequency of O.

Class intervals with exact limits:

Advantages of frequency polygon:

1. It is easy to draw and simple to understand.

2. It is possible to plot two distributions at a time on same axes.

3. Comparison of two distributions can be made through frequency polygon.

4. It is possible to make it smooth.

Limitations of frequency polygon:

1. It is less precise.

2. It is not accurate in terms of area the frequency upon each interval.

Uses of frequency polygon:

1. When two or more distributions are to be compared the frequency polygon is used.

2. It represents the data in graphic form.

3. It provides knowledge of how the scores in one or more group are distributed. Whether the

scores are piled up at the lower or higher end of the distribution or are evenly and regularly

distributed throughout the scale.

(Number of students) in the Y axis. Before plotting the graph we have to convert the c.i. into

their exact limits and extend one c.i. in each end with a frequency of O.

Class intervals with exact limits:

Advantages of frequency polygon:

1. It is easy to draw and simple to understand.

2. It is possible to plot two distributions at a time on same axes.

3. Comparison of two distributions can be made through frequency polygon.

4. It is possible to make it smooth.

Limitations of frequency polygon:

1. It is less precise.

2. It is not accurate in terms of area the frequency upon each interval.

Uses of frequency polygon:

1. When two or more distributions are to be compared the frequency polygon is used.

2. It represents the data in graphic form.

3. It provides knowledge of how the scores in one or more group are distributed. Whether the

scores are piled up at the lower or higher end of the distribution or are evenly and regularly

distributed throughout the scale.

9.
5.Cumulative Frequency Curve

Meaning:-This is a diagram that displays cumulative frequency.

To plot this graph first we have to convert, the class intervals into their exact limits. Then we

have to calculate the cumulative frequencies of the distribution.

Now we have to plot the cumulative frequencies in respect to their corresponding class-

Ogive plotted from the data given above:

1. Ogive is useful to determine the number of students below and above a particular score.

2. When the median as a measure of central tendency is wanted.

Meaning:-This is a diagram that displays cumulative frequency.

To plot this graph first we have to convert, the class intervals into their exact limits. Then we

have to calculate the cumulative frequencies of the distribution.

Now we have to plot the cumulative frequencies in respect to their corresponding class-

Ogive plotted from the data given above:

1. Ogive is useful to determine the number of students below and above a particular score.

2. When the median as a measure of central tendency is wanted.

10.
3. When the quartiles, deciles and percentiles are wanted.

4. By plotting the scores of two groups on a same scale we can compare both the groups.

6.Cumulative percentage Curve

Cumulative percentage is another way of expressing frequency distribution. It calculates the

percentage of the cumulative frequency within each interval, much as relative frequency

distribution calculates the percentage of frequency.

The main advantage of cumulative percentage over cumulative frequency as a measure of

frequency distribution is that it provides an easier way to compare different sets of data.

Cumulative frequency and cumulative percentage graphs are exactly the same, with the

exception of the vertical axis scale. In fact, it is possible to have the two vertical axes, (one for

cumulative frequency and another for cumulative percentage), on the same graph.

Cumulative percentage is calculated by dividing the cumulative frequency by the total number of

observations (n), then multiplying it by 100 (the last value will always be equal to 100%). Thus,

cumulative percentage = (cumulative frequency ÷ n) x 100

Example 1 – Calculating cumulative percentage

For 25 days, the snow depth at Whistler Mountain, B.C. was measured (to the nearest

centimeter) and recorded as follows:

242, 228, 217, 209, 253, 239, 266, 242, 251, 240, 223, 219, 246, 260, 258, 225, 234, 230, 249,

245, 254, 243, 235, 231, 257.

1. The snow depth measurements range from 209 cm to 266 cm. In order to produce the

table, the data are best grouped in class intervals of 10 cm each.

In the Snow depth column, each 10-cm class interval from 200 cm to 270 cm is listed.

The Frequency column records the number of observations that fall within a particular

interval. This column represents the observations in the Tally column, only in numerical

form.

Each of the numbers in the Endpoint column is the highest number in each class interval.

In the interval of 200 cm to 210 cm, the endpoint would be 210.

The Cumulative frequency column lists the total of each frequency added to its

predecessor, as seen in the exercises in the previous section.

The Cumulative percentage column divides the cumulative frequency by the total number

of observations (in this case, 25). The result is then multiplied by 100. This calculation

gives the cumulative percentage for each interval.

4. By plotting the scores of two groups on a same scale we can compare both the groups.

6.Cumulative percentage Curve

Cumulative percentage is another way of expressing frequency distribution. It calculates the

percentage of the cumulative frequency within each interval, much as relative frequency

distribution calculates the percentage of frequency.

The main advantage of cumulative percentage over cumulative frequency as a measure of

frequency distribution is that it provides an easier way to compare different sets of data.

Cumulative frequency and cumulative percentage graphs are exactly the same, with the

exception of the vertical axis scale. In fact, it is possible to have the two vertical axes, (one for

cumulative frequency and another for cumulative percentage), on the same graph.

Cumulative percentage is calculated by dividing the cumulative frequency by the total number of

observations (n), then multiplying it by 100 (the last value will always be equal to 100%). Thus,

cumulative percentage = (cumulative frequency ÷ n) x 100

Example 1 – Calculating cumulative percentage

For 25 days, the snow depth at Whistler Mountain, B.C. was measured (to the nearest

centimeter) and recorded as follows:

242, 228, 217, 209, 253, 239, 266, 242, 251, 240, 223, 219, 246, 260, 258, 225, 234, 230, 249,

245, 254, 243, 235, 231, 257.

1. The snow depth measurements range from 209 cm to 266 cm. In order to produce the

table, the data are best grouped in class intervals of 10 cm each.

In the Snow depth column, each 10-cm class interval from 200 cm to 270 cm is listed.

The Frequency column records the number of observations that fall within a particular

interval. This column represents the observations in the Tally column, only in numerical

form.

Each of the numbers in the Endpoint column is the highest number in each class interval.

In the interval of 200 cm to 210 cm, the endpoint would be 210.

The Cumulative frequency column lists the total of each frequency added to its

predecessor, as seen in the exercises in the previous section.

The Cumulative percentage column divides the cumulative frequency by the total number

of observations (in this case, 25). The result is then multiplied by 100. This calculation

gives the cumulative percentage for each interval.

11.
Snow depth (x) Frequency Endpoint Cumulative Cumulative percentage

(f) frequency

200 0 0 ÷ 25 x 100 = 0

200 to 210 1 210 1 1 ÷ 25 x 100 = 4

210 to 220 2 220 3 3 ÷ 25 x 100 = 12

220 to 230 3 230 6 6 ÷ 25 x 100 = 24

230 to 240 5 240 11 11 ÷ 25 x 100 = 44

240 to 250 7 250 18 18 ÷ 25 x 100 = 72

250 to 260 5 260 23 23 ÷ 25 x 100 = 92

260 to 270 2 270 25 25 ÷ 25 x 100 = 100

2. Apart from the extra axis representing the cumulative percentage, the graph should look

exactly the same as that drawn in Example 2 of the section on Cumulative frequency.

The Cumulative percentage axis is divided into five intervals of 20, while the Cumulative

frequency axis is divided into five intervals of 5. The Snow depth axis is divided by the

endpoints of each 10-cm class interval.

Using each endpoint to plot the graph, you will discover that both the cumulative

frequency and the cumulative percentage land in the same spot. For example, using the

endpoint of 260, plot your point on the 23rd day (cumulative frequency). This point

happens to be in the same place where the cumulative percentage (92%) will be plotted.

You have to be very careful when you are building a graph with two y-axes. For example,

if you have 47 observations, you might be tempted to use intervals of 5 and end your y-

axis at the cumulative frequency of 50. However, when you draw your y-axis for the

cumulative percentage, you must put the 100% interval at the same level as the 47 mark

on the other y-axis—not at the 50 mark. For this example, a cumulative frequency of

47 represents 100% of your data. If you put the 100% at the top of the scale where the

50 interval is marked, your line for the cumulative frequency will not match the line for the

cumulative percentage.

The plotted points join to form an ogive, which often looks similar to a stretched S. Ogives

are used to determine the number, or percentage, of observations that lie above or below

a specified value. For example, according to the table and the graph, 92% of the time the

snow depth recorded in the 25-day period was below the 260 cm mark.

(f) frequency

200 0 0 ÷ 25 x 100 = 0

200 to 210 1 210 1 1 ÷ 25 x 100 = 4

210 to 220 2 220 3 3 ÷ 25 x 100 = 12

220 to 230 3 230 6 6 ÷ 25 x 100 = 24

230 to 240 5 240 11 11 ÷ 25 x 100 = 44

240 to 250 7 250 18 18 ÷ 25 x 100 = 72

250 to 260 5 260 23 23 ÷ 25 x 100 = 92

260 to 270 2 270 25 25 ÷ 25 x 100 = 100

2. Apart from the extra axis representing the cumulative percentage, the graph should look

exactly the same as that drawn in Example 2 of the section on Cumulative frequency.

The Cumulative percentage axis is divided into five intervals of 20, while the Cumulative

frequency axis is divided into five intervals of 5. The Snow depth axis is divided by the

endpoints of each 10-cm class interval.

Using each endpoint to plot the graph, you will discover that both the cumulative

frequency and the cumulative percentage land in the same spot. For example, using the

endpoint of 260, plot your point on the 23rd day (cumulative frequency). This point

happens to be in the same place where the cumulative percentage (92%) will be plotted.

You have to be very careful when you are building a graph with two y-axes. For example,

if you have 47 observations, you might be tempted to use intervals of 5 and end your y-

axis at the cumulative frequency of 50. However, when you draw your y-axis for the

cumulative percentage, you must put the 100% interval at the same level as the 47 mark

on the other y-axis—not at the 50 mark. For this example, a cumulative frequency of

47 represents 100% of your data. If you put the 100% at the top of the scale where the

50 interval is marked, your line for the cumulative frequency will not match the line for the

cumulative percentage.

The plotted points join to form an ogive, which often looks similar to a stretched S. Ogives

are used to determine the number, or percentage, of observations that lie above or below

a specified value. For example, according to the table and the graph, 92% of the time the

snow depth recorded in the 25-day period was below the 260 cm mark.

12.
The following information can be gained from either the graph or table:

during the 25-day period, 24% of the time the recorded snow depth was less than

230 cm

on 7 of the 25 days, snow depth was at least 250 cm

during the 25-day period, 24% of the time the recorded snow depth was less than

230 cm

on 7 of the 25 days, snow depth was at least 250 cm