Let a, b in R . Let the mean and the variance of 6 observations -3,4,7,-6, a , b be 2 and 23 , respectively. The mean deviation about the mean of these 6 observations is :

Mathematics · Statistics

JEE Main 2024 — 4 April, Shift 1 — Question 13

Let $a, b \in R$ . Let the mean and the variance of 6 observations $-3,4,7,-6, \mathrm{a}, \mathrm{b}$ be 2 and 23 , respectively. The mean deviation about the mean of these 6 observations is :

Option A:
$\frac{13}{3}$
Correct
Option B:
$\frac{16}{3}$
Option C:
$\frac{11}{3}$
Option D:
$\frac{14}{3}$

Answer: A

Step-by-step solution

$\frac{\sum \mathrm{x}_{\mathrm{i}}}{6}=2$ and $\frac{\sum \mathrm{x}_{\mathrm{i}}^{2}}{\mathrm{~N}}-\mu^{2}=23$

$\alpha+\beta=10$

$\alpha^{2}+\beta^{2}=52$

solving we get $\alpha=4, \beta=6$

$\frac{\sum\left|\mathrm{x}_{\mathrm{i}}-\overline{\mathrm{x}}\right|}{6}=\frac{5+2+5+8+2+4}{6}=\frac{13}{3}$

Answer key and solution verified before publishing.

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Exam: JEE Main 2024
Paper: 4 April, Shift 1
Subject: Mathematics
Chapter: Statistics
Topic: Measures of Dispersion