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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