Question

The mean and S.D. of 1, 2, 3, 4, 5, 6 is

• A. $\frac{7}{2},\sqrt{\frac{35}{12}}$
• B. 3, 3
• C. $\frac{7}{2},\sqrt{3}$
• D. $3,\frac{35}{12}$

Answer 1

Answer: (A)

$\frac{7}{2},\sqrt{\frac{35}{12}}$

Answer 2

Mean $\bar{x} = \frac{1 + 2 + 3 + 4 + 5 + 6}{6} = \frac{21}{6} = \frac{7}{2}$

S.D. $= \sigma = \sqrt{\frac{1}{n}\Sigma x_{i}^{2} - (\bar{x})^{2}}$

$= \sqrt{\frac{1}{6}(1 + 4 + 9 + 16 + 25 + 36) - \frac{49}{4}}$

$= \sqrt{\frac{91}{6} - \frac{49}{4}} = \sqrt{\frac{182 - 147}{12}} = \sqrt{\frac{35}{12}}$.