Statistics Question 1
Question 1 - 2024 (01 Feb Shift 1)
Let the median and the mean deviation about the median of 7 observation $170,125,230,190,210, \mathrm{a}, \mathrm{b}$ be 170 and $\frac{205}{7}$ respectively. Then the mean deviation about the mean of these 7 observations is :
(1) 31
(2) 28
(3) 30
(4) 32
Show Answer
Answer (3)
Solution
$\text { Median }=170 \Rightarrow 125, \mathrm{a}, \mathrm{b}, 170,190,210,230$
Mean deviation about
Median $=$
$\frac{0+45+60+20+40+170-a+170-b}{7}=\frac{205}{7}$
$\Rightarrow \mathrm{a}+\mathrm{b}=300$
Mean $=\frac{170+125+230+190+210+a+b}{7}=175$
Mean deviation
About mean $=$
$\frac{50+175-a+175-b+5+15+35+55}{7}=30$
