Q. 64.8( 19 Votes )

# <span lang="EN-US

Answer : For median:

We have, total frequency, N = 100

N/2 = 100/2 = 50

Observe, cf = 76 is just greater than 50.

Thus, median class = 7-10

Median is given by Where,

L = Lower class limit of median class = 7

N/2 = 50

cf = cumulative frequency of the class preceding median class = 36

f = frequency of the median class = 40

h = class interval of the median class = 3

Substituting these values in the formula of median, we get  Median = 7 + 1.05

Median = 8.05

For mean:

Mean is given by  [Refer the values from the table given above]

Mean = 8.32

For mode:

Here, highest frequency is 40.

So, the modal class = 7-10

Mode is given by Where,

L = Lower class limit of the modal class = 7

h = class interval of the modal class = 3

f1 = frequency of the modal class = 40

f0 = frequency of the class preceding the modal class = 30

f2 = frequency of the class succeeding the modal class = 16

Substituting values in the formula of mode,  Mode = 7 + 0.88

Mode = 7.88

Thus, median is 8.05, mean is 8.32 and mode is 7.88.

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