1.  The following frequency distribution gives the monthly consumption of electricity of 68 consumers of a locality. Find the median, mean and mode of the data and compare them.

Let the assumed mean be a = 130 and h = 20

 Class Number of consumers Cumulative Frequency Class mark 65-85 4 4 70 -60 -3 -12 85-105 5 9 90 -40 -2 -10 105-125 13 22 110 -20 -1 -13 125-145 20 42 130 0 0 0 145-165 14 56 150 20 1 14 165-185 8 64 170 40 2 16 185-205 4 68 190 60 3 12 = 68 = 7

MEDIAN:

Median class = 125-145; Cumulative Frequency = 42; Lower limit, l = 125;

c.f. = 22; f = 20; h = 20

Thus, the median of the data is 137

MODE:

The class having maximum frequency is the modal class.
The maximum frequency is 20 and hence the modal class = 125-145
Lower limit (l) of modal class = 125, class size (h) = 20
Frequency () of the modal class = 20; frequency () of class preceding the modal class = 13, frequency () of class succeeding the modal class = 14.

Thus, Mode of the data is 135.76

MEAN:

Mean,

Thus, the Mean of the data is 137.05