Let the median and the mean deviation about the median of 7 observation 170,125,230,190,21…

Question

Let the median and the mean deviation about the median of 7 observation $170,125,230,190,210$, a, b be 170 and $\frac{205}{7}$ respectively. Then the mean deviation about the mean of these 7 observations is :

Accepted Answer

$$
\text { Median }=170 \Rightarrow 125, \mathrm{a}, \mathrm{b}, 170,190,210,230
$$

Mean deviation about
Median $=$

$$
\begin{aligned}
& \frac{0+45+60+20+40+170-a+170-b}{7}=\frac{205}{7} \\
& \Rightarrow \mathrm{a}+\mathrm{b}=300 \\
& \text { Mean }=\frac{170+125+230+190+210+a+b}{7}=175
\end{aligned}
$$

Mean deviation
About mean $=$

$$
\frac{50+175-a+175-b+5+15+35+55}{7}=30
$$

Solutions · 1