Question

The marks obtained by $9$ students in a chemistry test are $50,69,20,33,53,39,40,65$ and $59$ . If the mean deviation about the median of this data is $\lambda$ , then the value of $\frac{9\lambda }{10}$ is equal to

Answer 1

Answer: 11.4

$20,33,39,40,50,53,59,65,69$
Median, $M$ $={\left(\frac{9+1}{2}\right)}^{th}$ observation $=5^{th}$ observation $=50$
The absolute values of respective deviations from the median is
$30,17,11,10,0,3,9,15,19$
$\therefore \sum _{i=1}^9\left|x_i-M\right|=114$
Mean deviation about $M=\frac{1}{9}\sum _{i=1}^9\left|x_i-M\right|=\frac{1}{9}\times 114$
i.e $\lambda =\frac{114}{9}\Rightarrow \frac{9\lambda }{10}=11.4$