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 $=\frac{1}{n}\sum x_i^2-{\left(\overline{x}\right)}^2$
$=\frac{1}{8}\left[{\left(6\right)}^2+{\left(7\right)}^2+{\left(10\right)}^2+{\left(12\right)}^2+{\left(13\right)}^2+{\left(4\right)}^2+{\left(8\right)}^2+{\left(12\right)}^2\right]-81$
$=\frac{1}{8}\left[722\right]-81=90.25-81=9.25$