Which formula should be used to calculate the variance
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Variance is a statistical concept that measures the dispersion of a dataset. It is an essential measurement in fields like economics, engineering, psychology, and many others. As a result, knowing how to calculate variance accurately is crucial. There are two primary formulas that can be used for variance calculation: population variance and sample variance.
1.Population Variance
Population variance is the measure of dispersion of all data points within a given population. The formula for population variance (σ²) is:
σ² = Σ(x – μ)² / N
Where:
– σ² represents population variance
– Σ is the sum of the values
– x represents each individual data point
– μ is the mean (average) value of the entire population
– N is the total number of data points in the population
Use this formula when you’re working with a complete dataset — that is, you have information about every member of a population.
2.Sample Variance
Sample variance is the measure of dispersion for a subset (sample) of data points from a larger population. The formula for sample variance (S²) is:
S² = Σ(x – x̅)² / (n – 1)
Where:
– S² represents sample variance
– Σ is the sum of values
– x represents each sampled data point
– x̅ stands for the mean (average) value of the sample data points
– n denotes the total number of data points in the sample
Apply this formula when you only have information from a sample instead of from an entire population.
It’s essential to use the appropriate formula based on whether you are dealing with an entire dataset or just a representative subset. Using incorrect formulas in different situations may lead to inaccurate calculations and conclusions, thereby impacting your decision-making and analyses.
In summary, select the population variance formula (σ² = Σ(x – μ)² / N) when you have complete information for an entire population. Otherwise, opt for the sample variance formula (S² = Σ(x – x̅)² / (n – 1)) when working with representative subsets of a larger dataset.