Understanding Variance in Statistics | Calculation, Interpretation, and Differences between Population and Sample Variance

Variance Formula

The variance is a statistical measure of how spread out a set of data points are from their mean (average) value

The variance is a statistical measure of how spread out a set of data points are from their mean (average) value. It provides an indication of the variability or dispersion within a dataset. The formula for variance depends on whether you are calculating the population variance or the sample variance.

1. Population Variance (σ^2):
The population variance is used when you have data for the entire population. The formula for population variance is given by:

σ^2 = Σ(x – μ)^2 / N

Where:
– σ^2 is the population variance
– Σ represents the sum of
– x represents each individual data point
– μ is the mean of the population
– N is the total number of data points in the population

2. Sample Variance (s^2):
The sample variance is used when you only have a subset (sample) of data from a larger population. The formula for sample variance is similar to the population variance, but it has a slight modification to account for the degrees of freedom. The formula is:

s^2 = Σ(x – x̄)^2 / (n – 1)

Where:
– s^2 is the sample variance
– Σ represents the sum of
– x represents each individual data point in the sample
– x̄ is the sample mean
– n is the number of data points in the sample

In both formulas, the squared differences between each data point and the mean are summed up and divided by the appropriate denominator. As a result, the variance provides a quantitative measure of how much individual data points deviate from the central tendency (mean). A higher variance indicates greater variability, while a lower variance suggests less variability within the dataset.

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