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Question

Compute the mode of the following distribution:

Class interval0-1010-2020-3030-4040-5050-60
Frequency2510543

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Solution

Step 1: Finding different values of mode formula

Given table:

Class interval0-1010-2020-3030-4040-5050-60
Frequency2510543

From the above table, we can see that the class 20-30 has a maximum frequency, so the modal class is 20-30.

For determining the mode we will use the formula:

Mode=l+(f1-f02f1-f0-f2)×h

Where, l = Lower limit of modal class (20-30)=20

h = Size of the class-interval =10

f1 = Frequency of the modal class =10

f0 = Frequency of the class preceding the modal class =5

f2 = Frequency of the class succeeding the modal class =5

Step 2: Finding the mode

Substituting the values in the mode formula:

Mode=20+10-52×10-5-5×10=20+510×10=20+5

∴Mode=25

Hence, the mode of distribution is 25.


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