Variance Calculator - Calculator HD

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A Variance Calculator is a useful statistical tool that measures how far individual data points spread out from the mean. It helps users quickly determine the degree of variability within a dataset, whether for academic, professional, or analytical purposes. It is helpful for students, researchers, data analysts, and anyone working with numerical information. With clear inputs and instant results, a Variance Calculator simplifies complex statistical concepts and supports accurate, data-driven decision-making.

What Is Variance?

Variance is a statistical measure that shows how far each data point is from the mean and from every other data point. In simple terms:

Low variance = data points are close to the mean

High variance = data points are spread out

Variance is widely used in fields such as finance, machine learning, quality control, research, and risk analysis.

Mathematically, variance tells you how much dispersion exists in a dataset.

Variance Formula

Variance can be calculated in two ways, depending on the type of dataset you have.

Population Variance Formula

Population variance is used when you have data for the entire population.

σ^{2} = \frac{\sum_{}^{} {(x_{i} - μ)}^{2}}{N}

Where:

$σ$ = population standard deviation
$x_{i}$ = each data point
$μ$ = population mean
$N$ = total number of values

Sample Variance Formula

Sample variance is used when your dataset is a sample taken from a larger population.

s^{2} = \frac{\sum_{}^{} {(x_{i} - \overline{x})}^{2}}{n - 1}