Function Signature:
variance(sampleValues, mean=None)
Parameters:
sampleValues – The sample value. The outcomes of a random variable. The distribution for which the variance is to be computed. The parameter is any Python sequence or an iterable.
mean – The arithmetic mean of the sample. The default value is None. When the mean is not provided the function automatically calculates the Mean and uses it while calculating the variance.
Overview:
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The variance is given by the mean squared distance of the values from the mean of the distribution.
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It is a measure of dispersion. Variance describes how the values in a distribution is scattered or concentrated around the mean.
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Variance is the second moment of a distribution.
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The function variance() from the statistics module returns the sample variance.
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The Sample Variance s2 is given by the formula
s2 = i(1 to n)∑(xi-x̄)2/n-1
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Using (n-1) in the denominator of the variance calculation makes the Sample Variance an unbiased estimator of the Population Variance.
Exceptions:
Python raises a StatisticsError if the data passed inside the variance() function is empty.
Computing variance of a distribution:
The entries of the first column correspond to values of a distribution. The values are added and divided by the count of the distribution to get the mean value. The entries of the second column correspond to the squared distances from the mean. At the end of the second column squared distances from the mean are summed up and divided by the number of values in the distribution -1. This gives the sample variance.
| Sample Value(X) | Squared Distance From the mean(X-E(X))2 |
| 55 | 4.4567901234568 |
| 56 | 1.23456790123458 |
| 54 | 9.67901234567903 |
| 53 | 16.9012345679013 |
| 52 | 26.1234567901235 |
| 67 | 97.7901234567901 |
| 56 | 1.23456790123458 |
| 62 | 23.9012345679012 |
| 59 | 3.56790123456789 |
| Mean = SUM(x)/COUNT(x) = 57.11 |
Variance = (X-E(X))2/Count(X)-1 = 23.11 |
Example:
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# import the statistics module import statistics sampleData = [55,56,54,53,52,67,56,62,59] sampleVariance = statistics.variance(sampleData) print("Sample variance of the distribution is %.2f"%(sampleVariance)) |
Output:
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Sample variance of the distribution is 23.11 |