Q. 13.7( 26 Votes )

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Answer :

Let’s draw a table showing midpoints, frequencies and cumulative frequency. For median:

We have, total frequency, N = 68

N/2 = 68/2 = 34

Observe, cf = 42 is just greater than 34.

Thus, median class = 125-145

Median is given by Where,

L = Lower class limit of median class = 125

N/2 = 34

cf = cumulative frequency of the class preceding median class = 22

f = frequency of the median class = 20

h = class interval of the median class = 20

Substituting these values in the formula of median, we get Median = 125 + 12

Median = 137

For mean:

Mean is given by  Mean = 135 + 2.06

Mean = 137.06

For mode:

Here, highest frequency is 20.

So, the modal class = 125-145

Mode is given by Where,

L = Lower class limit of the modal class = 125

h = class interval of the modal class = 20

f1 = frequency of the modal class = 20

f0 = frequency of the class preceding the modal class = 13

f2 = frequency of the class succeeding the modal class = 14

Substituting values in the formula of mode,  Mode = 125 + 10.76

Mode = 135.76

Thus, median is 137, mean is 137.06 and mode is 135.76.

Median and mean, both gives us the average value of a data, with just the difference that mean can give us quantitative measure only but median can give us both quantitative as well as qualitative measure of a data. And that is why, mean and median have come out to be very close in this question.

Mode gives the value that appears most in a given data. Thus, the maximum monthly consumption of electricity is 135.76.

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