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 :

Mathematics · Statistics

JEE Main 2024 — 1 February, Shift 1 — Question 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 :

Option A:
31
Option B:
28
Option C:
30
Correct
Option D:
32

Answer: C

Step-by-step solution

Given observations: 170,125,230,190,210,a,b

Median = 170 ⇒ 4th term = 170

Arranging known values: 125,170,190,210,230

To keep median 170: a = 170

Given mean deviation about median = 205/7

So,

\sum |x_i -170| = 205

45+0+0+20+40+60+(170-b)=205

165+170-b=205

335-b=205

b=130

Mean:

\bar{x}=\frac{1225}{7}=175

Mean deviation about mean:

\frac{50+45+5+5+15+35+55}{7} =\frac{210}{7} =30

\boxed{30}

Answer key and solution verified before publishing.

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Exam: JEE Main 2024
Paper: 1 February, Shift 1
Subject: Mathematics
Chapter: Statistics
Topic: Measures of Dispersion