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Question

Find the mode of the given data:

Marks0-1010-2020-3030-4040-50
Frequency2024403620

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Solution

Find the mode of the data using mode formula

We are given a continuous set of data.

For the data, class interval with highest frequency is called as modal class 20-30 which have a frequency of 40.

We know that, mode=l+f1-f02f1-f0-f2h, where

l=lower limit of modal class

f1=frequency of the modal class

f0=frequency of the class preceding modal class

f2=frequency of the class succeeding modal class

h=size of the class interval

So, the mode for modal class 20-30 will be

⇒mode=20+40-24(2×40)-24-36×(30-20)⇒mode=20+1680-60×10⇒mode=20+16×1020⇒mode=20+8⇒mode=28

Hence, the mode of the data is 28.


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