If the variance of the frequency distribution x c 2c 3c 4c 5c 6c f 2 1 1 1 1 1 is 160, the…

Question

If the variance of the frequency distribution

$x$
 $c$
 $2c$
 $3c$
 $4c$
 $5c$
 $6c$

$f$
 2
 1
 1
 1
 1
 1

is 160, then the value of $c\in N$ is

Accepted Answer

${x}_{i}$
 $f({x}_{i})$
 $x(f(x)$
 ${x}^{2}f(x)$

C
 2
 2C
 2C${}^{2}$

2C
 1
 2C
 4C${}^{2}$

3C
 1
 3C
 9C${}^{2}$

4C
 1
 4C
 16C${}^{2}$

5C
 1
 5C
 25C${}^{2}$

6C
 1
 6C
 36C${}^{2}$

$\begin{gathered} {\sigma }^{2}=E({x}^{2})-[E(x)],\sum f({x}_{i})=7 \ E(x)=\sum xf(x)=22C \ E({x}^{2})=\sum {x}^{2}f(x)=92{C}^{2} \end{gathered}$

$\begin{gathered} {\sigma }^{2}=160=\frac{92{C}^{2}}{7}-{(\frac{22C}{7})}^{2} \ \Rightarrow C=\pm 7C\in N \ \Rightarrow C=7 \end{gathered}$

Solutions · 1