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Question

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.

Monthly~consumption~(in~units)Number~of~consumers6585485105510512513125145201451651416518581852054

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Solution

We may find the class marks by using the relation:

Class~mark=upper~class~limit~+~lower~class~limit2

Taking 135$as assumed mean a, we may find di,ui,fiui, according to step deviation method as following:

Monthly ConsuptionNumber of Consumers (fi)Class Mark(xi)di=xi135ui=di20fiui65854756031285105595402101051251311520113125145201350001451651415520114165185817540216185205419560312Total687

From the table, we may observe that:

fiui=7fi=68, class size h = 20, Mean ¯x=a+(fiuifi)×h=135+768×20=135+14068=137.058

Now, from table, it is clear that maximum class frequency is 20 belonging to class interval 125145.

Modal class = 125145

Lower limit l of modal class = 125

Class size h = 20

Frequency (f1) of modal class = 20

Frequency (f0) of class preceding modal class = 13

Frequency (f2) of class succeeding the modal class = 14

Mode=l+(f1f02f1f0f2)×h=125+[20132(20)1314]×20=125+713×20=125+14013=135.76

We know that:

3 median = mode + 2 mean

= 135.76+2(137.058)

= 135.76+274.116

= 409.876

Median = 136.625

So, median, mode, mean of given data is 136.625,135.76,137.05 respectively.


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