If the standard deviation of a set of numbers is 3.6, what is the variance?

Analyze the question: You're given the standard deviation (σ = 3.6) and asked for the variance.

Concept: Variance is the square of the standard deviation. Put the other way round, standard deviation is the square root of the variance.

Variance = (Standard deviation)²

Solution:

Variance = (3.6)²

3.6 × 3.6:

• 3.6 × 3 = 10.8
• 3.6 × 0.6 = 2.16
• 10.8 + 2.16 = 12.96

So the variance = 12.96

Check: √12.96 = 3.6, because 3.6 × 3.6 = 12.96. ✔

Tip: Variance and standard deviation are linked in a simple way, so remember "Variance = SD squared." When squaring a decimal, ignore the point first (36 × 36 = 1296), then put back two decimal places (one for each 3.6), giving 12.96. Also, the last digit of 3.6² must end in 6 because 6 × 6 = 36, which helps you rule out options A, B, C and E right away.