Question

The scores of $10$ students in a class test are given as $44,54,46,63,55,42,34,48,70,38$. Calculate the mean deviation about the median.

• A. $8.6$
• B. $6.6$
• C. $7.6$
• D. $8.8$
• E. $Noneofthese$

Answer 1

The correct option is A $8.6$

Arranging the scores of $10$ students in ascending order,

$34,38,42,44,46,48,54,55,63,70$

Number of students $=10$ (even)

$Median=\frac{1}{2}[{\left(\frac{10}{2}\right)}^{th}score+{(\frac{10}{2}+1)}^{th}score]$

$Median=\frac{1}{2}[5^{th}score+6^{th}score]$

$\therefore$ $Median=\frac{1}{2}[46+48]$

$\therefore$ $Median=47$

Mean deviation about median $=\frac{1}{n}\sum |x_i-M|$

$=\frac{|34-47|+|38-47|+|42-47|+|44-47|+|46-47|+|48-47|+|54-47|+|55-47|+|63-47|+|70-47|}{10}$

$=\frac{1}{10}(13+9+5+3+1+1+7+8+16+23)$

$=\frac{1}{10}\left(86\right)$

$=8.6$