Question 1

What is variance in simple terms

Accepted Answer

Variance measures how spread out data is from the mean. It's the average of squared differences from the mean.

Question 2

What's the difference between variance and standard deviation

Accepted Answer

Variance is in squared units, while standard deviation is in original units. Standard deviation = √variance, making it more interpretable.

Question 3

Why use (n-1) for sample variance

Accepted Answer

Using (n-1) instead of n (Bessel's correction) provides an unbiased estimate of the population variance from a sample.

Question 4

Can variance be negative

Accepted Answer

No, variance is always non-negative (≥ 0). It's zero only when all values are identical.

Question 5

What does high variance mean

Accepted Answer

High variance means data points are spread widely from the mean. Low variance means data is clustered closely around the mean.

Question 6

How do I calculate variance quickly

Accepted Answer

Use the computational formula: s² = [Σx² - (Σx)²/n] / (n - 1) for faster calculation with large datasets.

Question 7

What's variance of 0

Accepted Answer

Variance of 0 means all values in the dataset are identical. There's no variability.

Question 8

How does variance relate to standard deviation

Accepted Answer

Standard deviation is the square root of variance. If variance = 25, SD = 5.

Question 9

When should I use population vs sample variance

Accepted Answer

Use population variance when you have complete data. Use sample variance when you have a subset and want to estimate population variance.

Question 10

Why square the deviations

Accepted Answer

Squaring eliminates negative signs and gives more weight to larger deviations, providing a better measure of spread.

Practice Problems

Question 11

Beginner Level

Accepted Answer

Calculate variance: 2, 4, 6, 8, 10
Calculate variance: 10, 10, 10, 10
What's the variance of: 5, 5, 5, 5, 5?

Question 12

Intermediate Level

Accepted Answer

Calculate sample variance: 3, 7, 11, 15, 19
Calculate population variance: 1, 3, 5, 7, 9, 11
Find SD if variance = 64

Question 13

Advanced Level

Accepted Answer

Calculate variance: 12, 15, 18, 21, 24, 27
Which has higher variance: [5, 10, 15] or [8, 10, 12]?
If SD = 6, what's the variance?

Answers: [Click to reveal]

Beginner: 8, 0, 0
Intermediate: 35, 10, 8
Advanced: 24.5, [5, 10, 15] (Var ≈ 33.3 vs 5.3), 36

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