Question

The standard deviation of a given set of data is 20. If each of the value in the data is increased by 3, then the new standard deviation is .

• A. 17
• B. $23$
• C. 20
• D. $20+\sqrt{3}$

Answer 1

The correct option is C 20

$\mathrm{When}\mathrm{each}\mathrm{of}\mathrm{the}\mathrm{value}\mathrm{is}\mathrm{increased}\mathrm{by}3\mathrm{and}\mathrm{if}\mathrm{the}\mathrm{old}\mathrm{values}\mathrm{are}{x}_1,x_2,....,x_n,\mathrm{then}\mathrm{new}\mathrm{data}\mathrm{becomes}{x}_1+3,,...,x_n+3\mathrm{New}\mathrm{mean}=\frac{(x_1+3)+.....+(x_n+3)}{n}=\frac{x_1+...+x_n}{n}+\frac{3\times n}{n}=\mathrm{old}\mathrm{mean}+3\mathrm{But}(\mathrm{Mean}-x_i)\mathrm{remains}\mathrm{the}\mathrm{same}.\mathrm{Thus}\mathrm{variance}={\sum }^{}\frac{{\left(\mathrm{Mean}-x_1\right)}^2}{n}\mathrm{remains}\mathrm{the}\mathrm{same}.\mathrm{Hence}\mathrm{SD}=\sqrt{\mathrm{variance}}\mathrm{remains}\mathrm{the}\mathrm{same}.$