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

Answer 1

Daily Sales (X)	Days (​f)	fX	$\left|X\mathit{-}\overline{X}\right|\mathit{=}\left|d_{\overline{X}}\right|$	$\mathit{f}\left|d_{\overline{X}}\right|$ 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		∑$\mathit{f}\left|d_{\overline{X}}\right|$ = 1119.02	∑ = 3547.92

$$\begin{gathered} \mathrm{Mean}\left(\overline{X}\right)=\frac{{\sum }_{}fX}{{\sum }_{}f}=\frac{11298}{100}=112.98 \\ \mathrm{Mean}\mathrm{Deviation}\mathrm{from}\mathrm{mean}\left(M{D}_{\overline{X}}\right)=\frac{{\sum }_{}f{d}_{\overline{X}}}{{\sum }_{}f}=\frac{1119.02}{100}=11.19 \\ \mathrm{Standard}\mathrm{Deviation}\left(\sigma \right)=\sqrt{\frac{{\sum }_{}f{\left|X-\overline{X}\right|}^2}{{\sum }_{}f}}=\sqrt{\frac{3547.92}{100}}=5.96 \end{gathered}$$