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Cumulative Frequency Distribution

Cumulative Frequency Distribution

 

The data can be represented in the form of tables and frequencies. The cumulative frequency denotes the entire frequency within a frequency distribution table. These frequencies indicate the occurrence of those quantities or numbers against which they are placed. For example, if I say the frequency of number 5 is 8, the number 5 has occurred 8 times.

In statistics, the cumulative frequency can be found by adding the next class to its previous class. For example, the frequency of the third class will be the addition of the earlier two classes. The table that denotes cumulative frequency is known as a frequency distribution table.

Consider the following example. A manager has made records of his sales during the past few months after he joined the company. The data is represented below-

Month Number of profits (Frequency) Total profits (Cumulative Frequency)
January 10 10
February 40 10 + 40 = 50
March 75 50 + 75 = 125
April 98 125 + 98 = 223

One must note here that the last cumulative total will always be equal to the sum of all observations since all frequencies are already being added to the previous total. Here, 223 = 10 + 40 + 75 + 98.

How to construct a cumulative frequency table?

One can construct a cumulative frequency table using the following steps:
 1. Take the data of a continuous class of frequency distribution. It is easier to represent a continuous class in a cumulative frequency.
 2. Find the frequency of each class and denote it in front of the respective classes.
 3. Locate the upper and lower limit of every class.
 4. Record all the results of the frequency table by calculating the frequencies.

Example 1: Create a cumulative frequency table showing the number of days per month that Rani studies for her upcoming exams, using the given information:

Rani’s study time

Monday: 5 hrs

Tuesday: 6 hrs

Wednesday: 4 hrs

Thursday: 4 hrs

Friday: 6 hrs

Saturday: 7 hrs

Sunday: 7 hrs

Solution:

A cumulative frequency table for Rani’s study time can be made in the following manner:

Day Frequency (Hours) Cumulative Frequency (Hours)
Monday 5 5
Tuesday 6 5 + 6 = 11
Wednesday 4 11 + 4 = 15
Thursday 4 15 + 4 = 19
Friday 6 19 + 6 = 25
Saturday 7 25 + 7 = 32
Sunday 7 32 + 7 = 39

Rani spends 39 hours studying per week for her upcoming exams. We can cross the data by adding all the frequencies of the table, as 39 = 5 + 6 + 4 + 4 + 6 + 7 + 7.

Applications of cumulative frequency

 1) A cumulative frequency distribution is a representation of data that can denote large values of data.
 2) There is an upper and lower class by which we can calculate the frequencies easily.
 3) Cumulative frequency helps to observe the data and find out the particular number of observations lying below the particular range.
 4) By knowing the class of data, evaluation is easier.
 5) This is most widely used to denote marks of a class so that the performance of children can be known.

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