The mean of a data set is 10 and its standard deviation is 3. Each observation is multiplied by 2 and then increased by 3. The variance of the new…

Under $y=2x+3$, the mean becomes $23$ and the standard deviation is multiplied by $|2|$ only, giving $6$; the shift $+3$ does not change spread. The variance is therefore $6^2=36$. The value $9$ is the original variance, $18$ multiplies the variance by $2$ instead of $2^2$, and $12$ comes from adding the shift to the standard deviation. Variance scales by the square of the multiplier.