Question

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

Answer 1

Answer: 81

Given,${\sigma }_C=5$
Relation between${}^{\circ }C$ and ${}^{\circ }F$ is given by
$F=\frac{9C}{5}+32$
$\therefore {\sigma }_F=\frac{9}{5}{\sigma }_C=\frac{9}{5}\times 5=9$
Here,${\sigma }_F^2={\left(9\right)}^2=81$