Question

solv q no 9 and 10 in. a page​

Answer 1

(9).option "c"
(10).option"b"

Answer 2

$\bold{9.\: \bar{X} = \frac{x_1 + x_2 +....+ x_n}{n}}\\ \\ \bold{\bar{Y} = \frac{y_1 + y_2 +......+ y_n}{n}} \\ \\ \bold{Total\:terms\:we\:have\:n+n=2n} \\ \\ \bold{\tiny{\bar{Z} = \frac{x_1 + x_2 +....+ x_n + y_1 + y_2 +....+ y_n}{2n}}} \\ \\ \bold{\tiny{\bar{Z} = (\frac{x_1 + x_2 +....+ x_n}{n} + \frac{y_1 + y_2 +....+ y_n}{n}) \frac{1}{2}}} \\ \\ \bold{\bar{Z}= \frac{\bar{X} + \bar{Y}}{2}}$

$\bold{\Longrightarrow{Option\:(B)}}$

$\bold{10.\:\bar{X} = \frac{x_1 + x_2 +.....+ x_n}{n}} \\ \\ \bold{\tiny{If\:observation\:are\: ax_1 + ax_2 +...+ ax_n}} \\ \\ \bold{\frac{ax_1 + ax_2 +...+ ax_n}{n} = a\bar{X}} \\ \\ \bold{\tiny{If\:observation\:are\: \frac{x_1}{a}+\frac{x_2}{a}+...+\frac{x_2}{a}}} \\ \\ \bold{\frac{ \frac{x_1}{a}+\frac{x_2}{a}+...+\frac{x_2}{a}}{n}}= \frac{1}{a}\bar{X} \\ \\ \bold{So\:new\:mean:} \\ \\ \bold{\bar{X} = a\bar{X} + \frac{1}{a}\bar{X} = ( a + \frac{1}{a}) \bar{X}}$

$\bold{\Longrightarrow{Option\:(A)}}$