Question

The mean and the SD of $1,2,3,4,5,6$ are

• 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)

Mean $\bar{x}=\frac{1+2+3+4+5+6}{6}=\frac{21}{6}=\frac{7}{2}$
$SD=\sigma =\sqrt{\frac{1}{n}{\sum }_i^2-(\bar{x}{)}^2}$
$=\sqrt{\frac{1}{6}(1+4+9+16+25+36)-\frac{49}{4}}$
$=\sqrt{\frac{91}{6}-\frac{49}{4}}=\sqrt{\frac{182-147}{12}}$
$=\sqrt{\frac{35}{12}}$