Question

If the mean of 4, 7, 2, 8, 6 and a is 7, then the mean deviation from the median of these observations is

• A. 8
• B. 5
• C. 1
• D. 3

Answer 1

Answer: (D)

Given observations are 4, 7, 2, 8, 6, a and mean is 7.
We know
Mean = $\frac{4+7+2+8+6+a}{6}$
$\Rightarrow 7=\frac{4+7+2+8+6+a}{6}\Rightarrow a=15$
Now, given observations can be written in ascending order which is 2, 4, 6, 7, 8, 15
Since, No. of observation is even
$\therefore$ Median
$=\frac{\left(\frac{6}{2}\right)\text{th}\text{observation}+\left(\frac{6}{2}+1\right)\text{th}\text{observation}}{2}$
$=\frac{3\text{rd}\text{observation}+4\text{th}\text{observation}}{2}$
$=\frac{6+7}{2}=\frac{13}{2}$
Now, Mean deviation $=\frac{\sum _{i=1}^6|x_i-\frac{13}{2}|}{6}$
$=\frac{|4-\frac{13}{2}|+|7-\frac{13}{2}|+|2-\frac{13}{2}|+|8-\frac{13}{2}|+|6-\frac{13}{2}|+|15-\frac{13}{2}|}{6}$
$=\frac{\frac{5}{2}+\frac{1}{2}+\frac{9}{2}+\frac{3}{2}+\frac{1}{2}+\frac{17}{2}}{6}=\frac{18}{6}=3$