Question

# The table below shows the daily expenditure of food of 30 households in a locality: Daily expenditure (in Rs) Number of households 100-150 6 150-200 7 200-250 12 250-300 3 300-350 2 Find the mean and median daily expenditare on food.

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Solution

## We have the following: Daily income Mid value Frequency$\left({f}_{i}\right)$ Cumulative frequency ${f}_{i}×{x}_{i}$ 100-150 125 6 6 750 150-200 175 7 13 1225 200-250 225 12 25 2700 250-300 275 3 28 825 300-350 325 2 30 650 ∑${f}_{i}=30$ ∑$\left({f}_{i}×{x}_{i}\right)=$6150 Mean, $\overline{x}$=$\frac{\sum \left({f}_{i}×{x}_{i}\right)}{\sum {f}_{i}}$ =$\frac{6150}{30}$ =205 $\mathrm{Now},N=30\phantom{\rule{0ex}{0ex}}⇒\frac{N}{2}=15$ The cumulative frequency just greater than 15 is 25 and the corresponding class is 200-250. Thus, the median class is 200-250. $\mathrm{Now},l=200,h=50,f=12,c=cf$of preceding class = 13 and $\frac{N}{2}=15$ Median, ${M}_{e}=l+\left\{h×\frac{\left(\frac{N}{2}-c\right)}{f}\right\}$ $=200+\left\{50×\frac{\left(15-13\right)}{12}\right\}\phantom{\rule{0ex}{0ex}}=\left(200+50×\frac{2}{12}\right)$ =200 + 8.33 =208.33

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