JEE MAIN - Mathematics (2024 - 1st February Morning Shift - No. 7)
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 :
31
28
30
32
Explanation
$$
\text { Median }=170 \Rightarrow 125, \mathrm{a}, \mathrm{b}, 170,190,210,230
$$
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 $=$
$$ \frac{50+175-a+175-b+5+15+35+55}{7}=30 $$
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 $=$
$$ \frac{50+175-a+175-b+5+15+35+55}{7}=30 $$
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