Question

The standard deviation of some temperature data in ${}^{\circ }C$ is $5$. If the data were converted into ${}^{\circ }F$, the variance would be

• A. 81
• B. 57
• C. 36
• D. 25

Answer 1

The correct option is A 81

We know, ${}^{0}F={1.8}^{0}C+32$
also $S.D{(}^{0}C)=5$
$\therefore S.D{(}^{0}F)=S.D({1.8}^{0}C+32)=1.8\times S.D{(}^{0}C)=1.8\times 5=9$ (using fact $[S.D(ax+b)=|a|.S.D(x\left)\right]$)
Hence required variance $=9^2=81$