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Variance Calculator

Variance Calculator
s2 =
Standard Deviation
s =
n =
\( \overline{x} \) =
Sum of Squares
SS =

\[ s^{2} = \dfrac{\sum_{i=1}^{n}(x_i - \overline{x})^{2}}{n - 1} \]\[ s^{2} = \dfrac{SS}{n - 1} \]\[ s^{2} = ? \]For more detailed statistics use the
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Calculator Use

Variance is a measure of dispersion of data points from the mean. Low variance indicates that data points are generally similar and do not vary widely from the mean. High variance indicates that data values have greater variability and are more widely dispersed from the mean.

Enter a data set with values separated by spaces, commas or line breaks. You can also copy and paste your data from a document or a spreadsheet.

The variance calculator finds variance, standard deviation, sample size n, mean and sum of squares.

How to Calculate Variance

  1. Find the mean of the data set. Add all data values and divide by the sample size n.
  2. \( \overline{x} = \dfrac{\sum_{i=1}^{n}x_i}{n} \)
  3. Find the squared difference from the mean for each data value. Subtract the mean from each data value and square the result.
  4. \( (x_{i} - \overline{x})^{2} \)
  5. Find the sum of all the squared differences. The sum of squares is all the squared differences added together.
  6. \( SS = \sum_{i=1}^{n}(x_i - \overline{x})^{2} \)
  7. Calculate the sample variance. Variance is the sum of squares divided by sample size minus 1.
  8. \( s^{2} = \dfrac{\sum_{i=1}^{n}(x_i - \overline{x})^{2}}{n - 1} \)

Variance Formula

This calculator uses the variance formula for a population sample. The formula for variance s2 is the sum of the squared differences between each data point and the mean, divided by the number of data values n minus 1.

Variance = \( s^2 = \dfrac{\Sigma (x_{i} - \overline{x})^2}{n-1} \)

Standard deviation is the square root of the calculated variance of a sample data set.

Standard deviation = \( \sqrt {s^2} \)

You may come across the formula for population variance, σ2. This formula is used when the data for a parameter of an entire population is known. Note that instead of dividing by n-1, you divide by n.

Population Variance = \( \sigma^{2} = \dfrac{\sum_{i=1}^{n}(x_i - \overline{x})^{2}}{n} \)

The population standard deviation is the square root of the population variance.

Population Standard deviation = \( \sqrt {\sigma^2} \)

Cite this content, page or calculator as:

Furey, Edward "Variance Calculator"; CalculatorSoup, https://www.calculatorsoup.com - Online Calculators

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