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.
Solution:
Mean =
units
Modal class = (125-145)
Lower limit of the modal class
Size of the class interval
Frequency of the modal class
Frequency of the class proceeding the modal class
Frequency of the class succeeding the modal class
Mode
units
Number of consumers = 68
Cumulative frequency greater than
is 42
So, median class = 125-145
Median
where, l = lower limit of median class =125
n = number of observations =68
cf = cumulative frequency of class preceding the median class = 22
f = frequency of median class = 20
h = class size (assuming class size to be equal) = 20
Median
=125+12=137 units
Therefore, mean = 137.05 units, mode = 135.76 units and median = 137 units which are very close to each other.
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