If the variance of the frequency distribution is 160 , then the value of c in N is x c 2 c 3 c 4 c 5 c 6 c --- --- --- --- --- --- --- F 2 1 1 1 1 1

Mathematics · Statistics

JEE Main 2024 — 9 April, Shift 2 — Question 8

If the variance of the frequency distribution is 160 , then the value of $\mathrm{c} \in \mathrm{N}$ is

x	c	2 c	3 c	4 c	5 c	6 c
F	2	1	1	1	1	1

x	c	2 c	3 c	4 c	5 c	6 c
F	2	1	1	1	1	1

$\operatorname{Var}(\mathrm{x})=\frac{\mathrm{c}^{2}\left(2+2^{2}+3^{2}+4^{2}+5^{2}+6^{2}\right)}{7}-\left(\frac{22 c}{7}\right)^{2}$

$=\frac{92 c^{2}}{7}-c^{2} \times \frac{484}{49}$

$=\frac{(644-484) c^{2}}{49}=\frac{160 c^{2}}{49}$

$160=\frac{160 \times \mathrm{c}^{2}}{49} \Rightarrow \mathrm{c}=7$

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.