Sample Variance In Statistics For Better Data Analysis

Sample Variance ( measures spread )

s^2 = Σ(xi – x̄)^2 / (n – 1)

The sample variance is a statistical measure that describes how spread out the data in a sample is. It measures the average squared distance of each value from the sample mean. It is calculated by finding the sum of the squared differences between each data point and the sample mean, and then dividing it by the total number of data points in the sample minus one.

Mathematically, the formula for sample variance is:

s^2 = Σ(xi – x̄)^2 / (n – 1)

where
s^2 = sample variance
xi = individual data point
x̄ = sample mean
n = sample size

The sample variance is an essential measure that helps us understand how tightly or loosely a group of data is clustered around the mean. Higher values of sample variance indicate that the data is more spread out, while lower values indicate that it is more tightly clustered around the mean.

It is important to note that sample variance is a less biased estimate of the actual population variance, while its square root, the sample standard deviation, is a more interpretable measure as it is expressed in the same units as the original data.

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