Let the median and the mean deviation about the median of 7 observation 170, 125, 230, 190, 210, a, b be 170 and (205)/(7) respectively. Then the mean deviation about the mean of these 7 observations is:

Correct answer: C. 30 Given observations are 125, a, b, 170, 190, 210, 230 . Median = 170 Mean deviation about median is (205)/(7) . ⇒ (205)/(7) = (0 + 45 + 60 + 20 + 40 + 170 - a + 170 - b)/(7) ⇒ a + b = 300 Mean = (170 + 125 + 230 + 190 + 210 + a + b)/(7) = 175 Mean deviation about mean = (50 + 175 - a + 175 - b + 5 + 15 + 35 + 55)/(7) = 30

JEE Main 20241 FebruaryMorning Shift

Exam: JEE Main
Year: 2024
Date: 1 February
Shift: Morning Shift
Subject: Mathematics
Chapter: Statistics

JEE Main 2024 · 1 February · Morning Shift · Mathematics · Statistics

Let the median and the mean deviation about the median of 7...

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

Options

A $31$
B $28$
C $30$
D $32$

Correct answer

C. $30$

Step-by-step solution

Given observations are $125, a, b, 170, 190, 210, 230$ .

Median $= 170$

Mean deviation about median is $\dfrac{205}{7}$ .

$⇒ \dfrac{205}{7} = \dfrac{0 + 45 + 60 + 20 + 40 + 170 - a + 170 - b}{7}$

$⇒ a + b = 300$

Mean $= \dfrac{170 + 125 + 230 + 190 + 210 + a + b}{7} = 175$

Mean deviation about mean $= \dfrac{50 + 175 - a + 175 - b + 5 + 15 + 35 + 55}{7}$

$= 30$

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