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Question

# Following is the monthly income of eight families in a locality Monthly Income (₹) : 70, 10, 500, 75, 13, 250, 8, 42 Find out arithmetic mean using Direct Method and Short-cut Method.

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Solution

## Families Monthly income (X) Deviation from the Assumed average (d = X − A) (A = 75) 1 2 3 4 5 6 7 8 70 10 500 75 (A) 13 250 8 42 −5 −65 425 0 −62 175 −67 −33 (N) = 8 (ΣX)=968 Σd = −232 + 600 = 368 where, N= Number of items $\Sigma X$= Total of monthly income of all the families $\Sigma d$= net sum of deviations Calculation of Mean by Direct Method $\overline{)X}=\frac{\Sigma X}{N}=\frac{968}{8}=121$ Calculation of mean by short cut method $\overline{)X}=\mathrm{A}+\frac{\Sigma d}{N}\phantom{\rule{0ex}{0ex}}\mathrm{or},\overline{)X}=75+\frac{368}{8}\phantom{\rule{0ex}{0ex}}\mathrm{or},\overline{)X}=75+46\phantom{\rule{0ex}{0ex}}⇒\overline{)X}=121$ So, mean monthly income of a family is Rs 121.

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