What is variance and standard deviation?

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Variance and Standard Deviation are fundamental statistical measures used to understand the spread or dispersion of a data set.

Variance

Variance measures how far each number in a data set is from the mean (average). It tells us the degree of spread in the data. A higher variance means the data points are more spread out from the mean, while a lower variance indicates they are closer to the mean.

Formula for Variance (σ²):
For a population:
    σ² = Σ (xi - μ)² / N
Where:

• xi = each data point

• μ = population mean

• N = number of data points

For a sample:
    s² = Σ (xi - x̄)² / (n - 1)
Where x̄ is the sample mean and n is the sample size.

Standard Deviation

Standard Deviation is the square root of the variance. It provides the same information as variance but in the same unit as the data, making it more interpretable.

Formula:
    σ = √σ² or s = √s²

Example:

If a data set is: 2, 4, 6, 8
Mean = (2+4+6+8)/4 = 5
Variance = [(2−5)² + (4−5)² + (6−5)² + (8−5)²]/4 = (9+1+1+9)/4 = 5
Standard Deviation = √5 ≈ 2.24

Use in Real Life:

Standard deviation is used in finance, quality control, and scientific research to measure risk, consistency, and reliability.

In summary, variance shows how data points differ from the mean, while standard deviation gives a practical sense of that difference.

Read More:

What is the difference between population and sample?

Explain mean, median, mode.

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