Ogive (Cumulative Frequency Polygon)

Ogive graph tutorial
An ogive, also known as a cumulative frequency polygon, is a graph that shows how many data values lie above or below a certain value in a dataset.

To create an ogive, we use the cumulative frequencies in a frequency table. The way to find cumulative frequencies is to simply add the frequencies of each group that come before a certain value in a dataset.

Once we have a cumulative frequency table, we can create an ogive chart by charting the cumulative frequency points for each class interval and then connecting each of these points.

The following examples show how to create a cumulative frequency table from a raw set of data values as well as how to create an ogive graph using a cumulative frequency table.

Examples of Creating an Ogive Graph

Example 1

Create an ogive chart using the following set of data values:

3, 6, 7, 8, 12 ,13, 14, 14, 16, 22, 24, 26, 27, 33, 35, 37, 39, 40, 41, 47, 48, 49, 49, 49

Step 1: Create a frequency table

To create a frequency table, we need to decide on the class interval size, which is how wide the groups of data values will be. In this example, a class interval size of 10 seems reasonable. Next, we simply count how many data values fall into each interval:

Frequency table

Step 2: Find the cumulative frequency for each class interval

To find the cumulative frequency, we just add up each frequency going down the table. The first cumulative frequency is equal to itself, since we aren’t adding any other frequency to it, while the last cumulative frequency is equal to the total number of data values:

Cumulative frequency table
Step 3: Create an ogive chart.

To create an ogive chart, we simply need to place a dot at the ending value of each class interval  that represents the cumulative frequency up to that point. In addition, we need to place a dot on the starting value of the first class interval at value y = 0. Lastly, we need to connect all the dots with a line:

Ogive chart

Example 2

Create an ogive chart using the following set of data values:

2, 3, 3, 4, 5, 7, 8, 8, 9, 10, 11, 12, 13, 14, 14, 15, 15, 15, 17, 19, 19, 21, 22

Step 1: Create a frequency table

To create a frequency table, we need to decide on the class interval size, which is how wide the groups of data values will be. In this example, a class interval size of 5 seems reasonable. Next, we simply count how many data values fall into each interval:

Frequency table for example ogive chart

Step 2: Find the cumulative frequency for each class interval

To find the cumulative frequency, we just add up each frequency going down the table. The first cumulative frequency is equal to itself, since we aren’t adding any other frequency to it, while the last cumulative frequency is equal to the total number of data values:

Cumulative frequency table for ogive chart
Step 3: Create an ogive chart.

To create an ogive chart, we simply need to place a dot at the ending value of each class interval  that represents the cumulative frequency up to that point. In addition, we need to place a dot on the starting value of the first class interval at value y = 0. Lastly, we need to connect all the dots with a line:

Ogive example

How to Answer Questions Using an Ogive Graph

We can use ogive charts to answer interesting questions about data distributions.

Example 1

Consider the ogive chart below:

Ogive chart example
What percentage of values fall between 10 and 15?

The chart shows that a total of 10 values are less than 10 and 15 values are less than 15, so 15 – 10 = 5 values fall between 10 and 15.

How many values are greater than 15?

The chart shows that 15 values are less than 15 and that there are 24 total values (i.e. the maximum point on the y-axis). This means that 24 – 15 = 9 values are greater than 15.

How many values are greater than 10?

The chart shows that 10 values are less than 10 and that there are 24 total values. This means that 24 – 10 = 14 values are greater than 10.

Example 2

Consider the ogive chart below:

Ogive chart from cumulative frequency table

What is the minimum and maximum value in this dataset?

The minimum value in the dataset is 1 since this is where the ogive chart starts on the x-axis. The maximum value in the dataset is 10 since this is where the ogive chart ends on the x-axis. 

How many values are greater than 7?

The chart shows that 15 values are less than 7 and that there are 24 total values (i.e. the maximum point on the y-axis). This means that 24 – 15 = 9 values are greater than 7.

How many values are between 2 and 7?

The chart shows that 5 values are less than 2 and 15 values are less than 7, so 15 – 5 = 10 values fall between 2 and 7.

How to Create an Ogive Graph in Excel

To create an ogive chart in Excel, simply follow the steps below:

Step 1: Type the values of your dataset into one column.

Type in the values of your dataset into one column in Excel. For this example, I choose to type the 24 values in my dataset in column A:

Ogive chart in Excel

Step 2: Choose your class interval size.

Decide on a class interval size. For this dataset, I choose a class interval size of 10. Next, I simply type in my class interval start and end values in columns C and D:

Ogive example in Microsoft Excel

Step 3: Find the frequencies and cumulative frequencies

Type the following formulas in columns F and G:

Ogive chart formula in Excel
For the dataset I’m working with in this example, these formulas will produce the following values:

Ogive chart frequency table in Excel

Step 4: Create the ogive chart

Copy and paste the class ending values in column I and the cumulative frequencies in column J:

Note: I also added a class end of “0” with a cumulative frequency of “0” to ensure the chart starts at zero.

Ogive in Excel

To create the ogive chart, highlight the data in columns I and J. Then, on the INSERT tab, in the Charts Group, click Scatter Chart, then click Scatter with Straight Lines and Markers:

Ogive in Excel
Once you click this, an ogive chart will automatically be generated:

Finished ogive chart in Excel
Feel free to modify the colors, chart title, axes titles, and axes labels to make the chart look however you would like.

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