If the standard deviation of a given data is 8.2, find its variance_______________

Analyze the question

You are given the standard deviation (σ = 8.2) and asked for the variance.

Concept

Variance is the square of the standard deviation:

Variance = (Standard deviation)² = σ²

(Equivalently, standard deviation = √variance.)

Solution

Variance = (8.2)²

8.2 × 8.2:

• 8 × 8.2 = 65.6
• 0.2 × 8.2 = 1.64
• Total = 65.6 + 1.64 = 67.24

So the variance ≈ 67.24, which is about 67.2.

Checking the other options

• A (82.0) would come from multiplying 8.2 by 10, which has no statistical basis.
• B (91.8) does not correspond to any correct operation.
• D (4.1) is half of 8.2, which is wrong. Dividing by 2 has nothing to do with variance.

Answer: C (67.2)

Exam tip

Remember: "Variance is the square, standard deviation is the root." If a question gives you the variance and asks for the standard deviation, take the square root. If it gives you the standard deviation and asks for the variance, square it. For quick estimation, 8² = 64 and 9² = 81, so the answer must lie between 64 and 81, and only option C fits that range.