Let the mean and the standard deviation of the observation 2,3,3,4,5,7, a, b be 4 and √(2) respectively. Then the mean deviation about the mode of these observations is :

Mathematics · Statistics

JEE Main 2025 — 4 April, Evening Shift — Question 33

Let the mean and the standard deviation of the observation $2,3,3,4,5,7, a, b$ be 4 and $\sqrt{2}$ respectively. Then

the mean deviation about the mode of these observations is :

$\frac{2+3+3+4+5+7+a+b}{8}=4$

$\Rightarrow a+b=8$

$(\sqrt{2})^{2}=\frac{2^{2}+3^{2}+3^{2}+4^{2}+5^{2}+7^{2}+a^{2}+b^{2}}{8}-16$ $112+a^{2}+b^{2}=18 \times 8$

$\Rightarrow a^{2}+b^{2}=32$

$\Rightarrow a=b=4$ Now numbers be $2,3,3,4,4,4,5,7$

Mode $=4$ Mean deviation about mode :

\frac{|2-4|+|3-4|+|3-4|+0+0+0+|5-4|+|4-7|}{8}

=\frac{2+1+1+1+3}{8}=\frac{8}{8}=1

Answer key and solution verified before publishing.

Start with this question, then two more from the same chapter — with a tutor that explains every step. Free.