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

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

Accepted Answer

$$7 = \frac{4+7+2+8+6+a}{6} \implies a=15$$

Ascending order: $2,4,6,7,8,15$. Median $= \dfrac{6+7}{2}=\dfrac{13}{2}$

$$\text{M.D.} = \frac{|4-6.5|+|7-6.5|+|2-6.5|+|8-6.5|+|6-6.5|+|15-6.5|}{6} = \frac{2.5+0.5+4.5+1.5+0.5+8.5}{6}=\frac{18}{6}=3$$

Solutions · 1