DzaWeb: Statistical graphs – Cumulative Frequency (Ogive)

Introduction

Having organized the data into a frequency distribution, you need to present them in graphical form. The purpose of graph in statistics is to convey the data to the viewers into pictorial form. The reason is that it is easier for most people to understand the meaning of data presented graphically than data presented numerically in frequency distributions or tables. This is especially true if users have little or no statistical knowledge.

Uses of statistical graphs

1. Statistical graphs can be used to analyse a data or described it.

2. They are used to get the audience’s attention in a speaking presentation.

3. They are also used to discover a pattern in a situation over a period of time.

4. Statistical graphs are used to summarize a data.

The Ogive:

This type of graph is called cumulative frequency graph, or ogive. The cumulative frequency is the sum of the frequencies accumulated up to the upper boundary of a class in the distribution. The graph is drawn by plotting the cumulative frequency on the vertical axis against the upper class boundary [marks less that, less than class etc] on the horizontal axis.

Definition: The Ogive is a graph that represents the cumulative frequencies for the classes in a frequency distribution.

The example below shows the procedure for constructing an ogive.

Example one:

The following table shows the distribution of the marks scored by 200 candidates in an examination.

Marks	0-9	10-19	20-29	30-39	40-49	50-59	60-69	70-79	80-89
Frequency	3	18	20	25	34	50	25	15	10

Construct a cumulative frequency table and use it to draw a cumulative frequency curve for the distribution.

Solution

Steps:

1. Find the cumulative frequency for each class.

2. Draw the x and y axes. Label the x axis with the upper class boundaries. Use an appropriate scale for the y axis to represent the cumulative frequencies. (Depending on the numbers in cumulative frequency columns, scales such as 0,1,2,.., or 5,10,15,... can be used. Do not label the y axis with the number in the cumulative frequency column.) In this example, a scale of 0, 20, 40, 60 ... will be used.

3. Plot the cumulative frequency at each upper class boundary. Upper boundaries are used since the cumulative frequencies represent the number of data values accumulated up to the upper boundary of each class.

4. Starting with the first upper boundary, connect adjacent points with line segments. Then extend the graph to the first lower class boundary, on the x-axis.