# The table below shows the daily expenditure on food of 25 households in a locality.  Daily expenditure (in Rs): 100 -150, 150 - 200

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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