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Question

Data of daily sale proceeds of a shop are as below. Calculate mean deviation and standard deviation. Daily Sales 102 100 110 114 118 122 126 Days 3 9 25 35 17 10 1

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Solution

Daily Sales (X) Days (​f) fX $\left|X\mathit{-}\overline{)X}\right|\mathbit{=}\left|{d}_{\overline{)X}}\right|$ $\mathbit{f}\left|{d}_{\overline{)X}}\right|$ or $f\left|X\mathit{-}\overline{)X}\right|$ $f{\left|X\mathit{-}\overline{)X}\right|}^{2}\mathrm{or}f{\left|{\mathit{d}}_{\overline{)\mathit{X}}}\right|}^{2}$ 102 100 110 114 118 122 126 3 9 25 35 17 10 1 306 900 2750 3990 2006 1220 126 10.98 12.98 2.98 1.02 5.02 9.02 13.02 32.94 116.82 745 35.7 85.34 90.2 13.02 361.68 1516.32 222 36. 428.4 813.6 169.52 ∑f = 100 ∑fX = 11298 ∑$\mathbit{f}\left|{d}_{\overline{)X}}\right|$ = 1119.02 ∑ = 3547.92 $\mathrm{Mean}\left(\overline{)X}\right)=\frac{{\sum }_{}fX}{{\sum }_{}f}=\frac{11298}{100}=112.98\phantom{\rule{0ex}{0ex}}\mathrm{Mean}\mathrm{Deviation}\mathrm{from}\mathrm{mean}\left(M{D}_{\overline{)X}}\right)=\frac{{\sum }_{}f{d}_{\overline{)X}}}{{\sum }_{}f}=\frac{1119.02}{100}=11.19\phantom{\rule{0ex}{0ex}}\mathrm{Standard}\mathrm{Deviation}\left(\sigma \right)=\sqrt{\frac{{\sum }_{}f{\left|X-\overline{)X}\right|}^{2}}{{\sum }_{}f}}=\sqrt{\frac{3547.92}{100}}=5.96$

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