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# The table below shows the daily expenditure on food of 25 households in a locality. Find the mean daily expenditure on food by a suitable method. Daily expenditure(in Rs) 100-150 150-200 200-250 250-300 300-350 Number of households 4 5 12 2 2

Let us assume the mean (A) = 225, Class size (h) = 50

 Class Interval Number of households $$( f_i )$$ Mid-point $$( x_i )$$ $$d_i \ = \ x_i \ - \ A$$ $$u_i \ = \ \frac{d_i}{50}$$ $$f_i u_i$$ 100-150 4 125 -100 -2 -8 150-200 5 175 -50 -1 -5 200-250 12 225 0 0 0 250-300 2 275 50 1 2 300-350 2 325 100 2 4 $$\sum f_i \ = \ 25$$ $$\sum f_i u_i \ = \ -7$$

$$\overline{x} \ = \ A \ + h \frac{ \sum \ f_i u_i}{ \sum f_i}$$

$$= \ 225 \ + \ 50 × \frac{-7}{25}$$

$$= \ 225 \ - \ 14 \ = \ 211$$

$$\therefore$$ The mean daily expenditure on food is 211