# When tested , the lives (in hours) of $5$ bulbs were noted as follows : $1357,1090,1666,1494,1623$ The mean deviations (in hours) from their mean is

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

Toolbox:
• 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.