A dataset has mean 1 and variance 0.01. Find the mean and variance after every value is multiplied by 10.

01 / Standard#Your turn

Official paper · jm01-2021 · I.13 · PDF 3

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

The mean scales linearly.

Hint 2

Squared deviations scale by the square of the multiplier.

Worked solution

Transform the mean.
$\overline{10x}=10\bar x=10$
Transform the variance.
$\operatorname{Var}(10X)=10^2\operatorname{Var}(X)=100(0.01)=1$

D: mean 10, variance 1.

Checks and common pitfalls: Standard deviation scales by 10, but variance scales by 100.

Reasoning checklist · self / teacher assessment

Teaching assessment checklist, independently authored. Use the original paper for official marks.
Transform the mean.
$\overline{10x}=10\bar x=10$
Transform the variance.
$\operatorname{Var}(10X)=10^2\operatorname{Var}(X)=100(0.01)=1$

Think first. Reveal a hint when the class is ready.

2021 JM01