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The table below shows the daily expenditure on food of 25 households in a locality.

 Daily expenditure (in Rs):  100 - 150  150 - 200  200 - 250  250 - 300  300 - 350
 Number of households:  4  5  12  2  2

Find the mean daily expenditure on food by a suitable method.

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We may calculate class marks (xi) for each interval by using the relation

xi \(=\frac{Upper\,class\,limit+lower\,class\,limits}{2}\)

Class size = 50

Now taking 225 as assumed mean we can calculate as follows:

 Daily expenditure (in Rs)  fi  di = xi - A = xi - 225 ui \(\frac{xi-225}{h}\) xi fiui
 100 - 150 4 -100 -2 125 -8
 150 - 200 5 -50 -1 175 -5
 200 - 250 12 0 0 225 0
 250 - 300 2 50 1 275 2
 300 - 350 2 100 2 325 4
 N = 25 \(\sum\)fiui = -7

Mean (x̅) = A + \(\frac{\sum f_iu_i}{N}\times h\) 

\(=225+\frac{-7}{25}\times50\)

\(=225-14=211\)

So mean expenditure on food is 211

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