Let’s draw a table showing midpoints, frequencies and cumulative frequency.
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
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
Mean is given by
⇒ Mean = 135 + 2.06
⇒ Mean = 137.06
Here, highest frequency is 20.
So, the modal class = 125-145
Mode is given by
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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