Question

Calculate the standard Deviation of wage earner's daily earnings:

Week	:	1	2	3	4	5	6	7	8	9	10
Earnings (in ₹)	:	54	62	63	65	68	71	73	78	82	84

Answer 1

S.No. (Week)	Farming (X)	Deviation $\left(X\mathit{-}\overline{\mathit{X}}\right)$ $\left(\overline{\mathit{X}}=70\right)$	Square of deviation ${\left(X\mathit{-}\overline{\mathit{X}}\right)}^2$
1 2 3 4 5 6 7 8 9 10	54 62 63 65 68 71 73 78 82 84	−16 −8 −7 −5 −2 1 3 8 12 14	256 64 49 25 4 1 9 64 144 196
	ΣX = 700		$\mathrm{\Sigma }{\left(\mathit{X}\mathit{-}\overline{\mathit{X}}\right)}^2=812$

The mean of the given series can be calculated in the following manner.
$\overline{X}=\frac{\Sigma X}{N}=\frac{700}{10}=70$
To calculate standard deviation, we use the following formula.
$$\begin{gathered} SD\left(\sigma \right)=\sqrt{\frac{\mathit{\Sigma }{\left(\mathit{X}\mathit{-}\overline{\mathit{X}}\right)}^{\mathit{2}}}{\mathit{N}}} \\ \mathrm{Putting}\mathrm{the}\mathrm{vaules}\mathrm{we}\mathrm{get}, \\ SD\left(\sigma \right)=\sqrt{\frac{812}{10}}=\sqrt{81.2}=9.01 \end{gathered}$$
Thus, standard deviation of wage earner's daily earnings is 9.01.