Question

The mean of $5$ observation is $6$ and the varience is $\mathrm{6.80.}$ If three of the five observation are $8,5$ and $10.$ Then the remaining two observation are

• A. $0\text{and}7$
• B. $5\text{and}2$
• C. $1\text{and}6$
• D. $3\text{and}4$

Answer 1

The correct option is D $3\text{and}4$

$\sum x_i=n.\overline{x}=5\times 6=30$
$\sum x_i=a+b+8+5+10+x+y=30\Rightarrow a+b=7...\left(i\right)$

${\sigma }^2=\frac{\sum x_i^2}{5}-(\overline{x}{)}^2$
$\Rightarrow 6.8=\frac{\sum x_i^2}{5}-6^2$
$\Rightarrow \sum x_i^2=a^2+b^2+8^2+5^2+{10}^2=42.8\times 5$

using equation $\left(i\right)$
$\Rightarrow a^2+(7-a{)}^2=214-189=25$
$\Rightarrow 2a^2-14a+24=0$
$\therefore a=3,4$