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Question: Define cumulative frequency distribution....

Define cumulative frequency distribution.

Explanation

Solution

Here we have to define the term, cumulative frequency distribution. The frequency distribution is an overview or a representation of all distinct values corresponding to some variable and the number of times they occur. It represents the frequency within the given class interval or the number of observations occur within the given class interval.

Complete step by step solution:
A cumulative frequency distribution is a type of frequency distribution which represents the sum of a frequency of a class and all classes below it. The cumulative frequency distribution is very helpful in determining the frequency up to a certain threshold. We will now draw the frequency distribution table with appropriate data and we will find the cumulative frequency.
The following table is a frequency distribution of 20 objects.

Mass (g)10-1415-1920-2425-29
frequency5429

We will find the cumulative frequency now.
First we will calculate the cumulative frequency for class intervals 10−1410 - 14.
The cumulative frequency of the class interval 10−1410 - 14 is the same as the given frequency as there is no class below it.
Cumulative frequency of class interval 15−1915 - 19 is equal to the sum of frequency of class interval 10−1410 - 14and its own frequency
Therefore,
Cumulative frequency of class interval15 - 19$$$$ = 5 + 4 = 9
Similarly,
Cumulative frequency of class interval 20−2420 - 24 is equal to the sum of frequency of class interval 10−1410 - 14, class interval 15−1915 - 19, and its own frequency.
Therefore,
Cumulative frequency of class interval 20 - 24$$$$ = 5 + 4 + 2 = 11
Cumulative frequency of class interval 25−2925 - 29 is equal to the sum of frequency of class interval 20−2420 - 24, class interval 10−1410 - 14, class interval 15−1915 - 19, and its own frequency.
Therefore,

Cumulative frequency of class interval 25 - 29$$$$ = 5 + 4 + 2 + 9 = 20

Note:
Cumulative frequency of any class is calculated using its corresponding frequency. A cumulative frequency distribution table is drawn after drawing a frequency distribution table. It is used to analyze and understand large amounts of information.