Question

The mean and variance for the data $6, 7, 10, 12, 13, 4, 8, 12$ respectively are

• A. $ 8 , \sqrt{26.25} $
• B. $9 , \sqrt{9.25} $
• C. 8, 26.25
• D. 9, 9.25

Answer 1

Answer: (D)

Data is 6, 7, 10, 12, 13, 4, 8, 12
$n = 8$
$\therefore $ Mean = $ \bar{x} = \frac{6+7+10+12+13+4+8+12}{8}$
$= \frac{72}{8} = 9 $
Now, Variance $=\frac{1}{n} \sum x_{i}^{2} -\left(\overline{x}\right)^{2}$
$ = \frac{1}{8}\left[\left(6\right)^{2}+\left(7\right)^{2}+\left(10\right)^{2}+\left(12\right)^{2}+\left(13\right)^{2}+\left(4\right)^{2}+\left(8\right)^{2 }+\left(12\right)^{2}\right]-81$
$= \frac{1}{8} \left[722\right]-81=90.25-81=9.25$