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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


Answer :

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

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