Question

The following are the marks obtained by 9 students in Mathematics test: 50, 69, 20, 33, 53, 39, 40, 65, 59. The mean deviation from the median is
(a) 9
(b) 10.5
(c) 12.67
(d) 14.67

Answer 1

Given marks of 9 students in Mathematics test 50, 69, 20, 33, 53, 39, 40, 65, 59
Arranging the observations in ascending order 20, 33, 39, 40, 50, 53, 59, 65, 69

Since n is odd,
∴ median is ${\left(\frac{n+1}{2}\right)}^{\mathrm{th}}$ term
i.e 50 is the median.
Calculation of mean deviation

xi	$\left|d_i\right|=\left|x_i-50\right|$
20 33 39 40 50 53 59 65 69	30 17 11 10 0 3 9 15 19
	$\mathrm{\Sigma }{d}_i=114$

$\therefore \mathrm{Mean}\mathrm{deviation}\mathrm{is}\frac{1}{n}\mathrm{\Sigma }{d}_i=\frac{114}{9}=12.67$

Hence, the correct answer is option C.