The mean of the numbers a, b,8,5 and 10 is 6 and the variance is 6.80. Then, which one of the following gives possible values of a and b?

# The mean of the numbers a, b,8,5 and 10 is 6 and the variance is 6.80. Then, which one of the following gives possible values of a and b?

1. A

a=3,b=4

2. B

a=0,b=7

3. C

a=5,b=2

4. D

a=1,b=6

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### Solution:

According to the given condition,

$\begin{array}{l} \\ \\ 6.80=\frac{\left[\begin{array}{c}\left(6-\mathrm{a}{\right)}^{2}+\left(6-\mathrm{b}{\right)}^{2}+\left(6-8{\right)}^{2}\\ +\left(6-5{\right)}^{2}+\left(6-10{\right)}^{2}\end{array}\right]}{5}\\ ⇒ 34=\left(6-\mathrm{a}{\right)}^{2}+\left(6-\mathrm{b}{\right)}^{2}+4+1+16\\ ⇒ \left(6-\mathrm{a}{\right)}^{2}+\left(6-\mathrm{b}{\right)}^{2}=13=9+4\\ ⇒ \left(6-\mathrm{a}{\right)}^{2}+\left(6-\mathrm{b}{\right)}^{2}={3}^{2}+{2}^{2}\\ ⇒ \mathrm{a}=3,\mathrm{b}=4\end{array}$

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