$\begin{array}{1 1}(A)\;178\\(B)\;179\\(C)\;220\\(D)\;356\end{array} $

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- The formulae to solve the problem are Mean $=\large\frac{\sum x_i}{n} $
- Mean deviation about mean = $ \large\frac{\sum|x_i -\bar{x}|}{n}$

Mean of the given series

$\bar{x}=\large\frac{\text{sum of the terms}}{\text{number of terms}} $

$\quad= \large\frac{\sum x_i}{n}$

$\quad= \large\frac{ 1357+1090+1666+1494+1623}{5}$

$\quad= \large\frac{7230}{5}$

$\qquad= 1446$

$x_i =1357 ; \qquad |x_i -\bar {x} | =|1357 -1446|=89$

$x_i =1090 ; \qquad |x_i -\bar {x} | =|1090 -1446|=356$

$x_i =1666 ; \qquad |x_i -\bar {x} | =|1666 -1446|=220$

$x_i =1494 ; \qquad |x_i -\bar {x} | =|1494 -1446|=48$

$x_i =1623 ; \qquad |x_i -\bar {x} | =|1623 -1446|=177$

Total = 890

Mean deviation about mean = $ \large\frac{\sum|x_i -\bar{x}|}{n}$

$\qquad= \large\frac{890}{5}$$=178 (hours)$

Hence a is the correct answer.

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