Standard Deviation and Variance Calculator

Standard deviation is used in statistics. It shows how data is spread. Standard deviation and variance are very important in studies and real life.

What is Variance?

Variance tells how far numbers are from the mean. It is the average of squared differences from the mean.

Formula for population variance:
σ⊃2; = Σ (x - μ)⊃2; / N

Formula for sample variance:
s⊃2; = Σ (x - x̄)⊃2; / (n - 1)

• x = each value

• μ = population mean

• x̄ = sample mean

• N = population size

• n = sample size

What is Standard Deviation?

Standard deviation is the square root of variance. It tells you how far the numbers are spread out.

Formula for population standard deviation:
σ = √σ⊃2;

Formula for sample standard deviation:
s = √s⊃2;

Example:
Variance = 2.67
Standard deviation = √2.67 = 1.63

Relation between Variance and Standard Deviation

• Variance is the average of squared differences.

• Standard deviation is the result of the square root of variance.

• Variance is in squared units.

• Standard deviation is in the same unit as the data.

When to Use Variance and Standard Deviation

• Use variance in calculations.

• Use standard deviation to explain results.

Applications

• Finance → To measure risk in investment.

• Production → To check the quality of products.

• Education → To study exam scores.

• Research → To measure spread in experiments.

Conclusion

Variance and standard deviation are fundamental tools in statistics. Variance shows spread in squared form. Standard deviation shows the spread in a simple form. Both are important to understand data.