In a given set of data, if the variance is 25, what is the standard deviation?

Analyze the question You are given the variance (25) and asked for the standard deviation.

Concept The standard deviation is the positive square root of the variance:

σ = √(variance)

Variance is the average of the squared deviations from the mean, so taking the square root brings the measure back to the original units of the data.

Solution Variance = 25

Standard deviation = √25 = 5

Check against the options

• A. 45: not the square root of 25
• B. 5: 5 × 5 = 25 ✔
• C. 55: no
• D. 10: 10 × 10 = 100, not 25 (a common mistake is halving 25 or mixing it up with 2 × 5)
• E. 12: no

Tip Remember: Standard deviation is the square root of variance, and variance is the square of standard deviation. Learn your perfect squares (1, 4, 9, 16, 25, 36, 49, ...) so you can answer these in seconds in the exam.