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Variance measures how far a set of data is spread out. A variance of zero indicates that all of the data values are identical. All non-zero variances are positive. |
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A small variance indicates that the data points tend to be very close to the mean, and to each other. A high variance indicates that the data points are very spread out from the mean, and from one another. Variance is the average of the squared distances from each point to the mean.
The process of finding the variance is very similar to finding the MAD, mean absolute deviation.
The only difference is the squaring of the distances.
Process: (1) Find the mean (average) of the set. (2) Subtract each data value from the mean to find its distance from the mean. (3) Square all distances. (4) Add all the squares of the distances.
(4) Divide by the number of pieces of data (for population variance). |
One problem with the variance is that it does not have the same unit of measure as the original data. For example, original data containing lengths measured in feet has a variance measured in square feet.
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Don't ROUND too soon! When working with the formulas for variance and standard deviation, be careful to avoid rounding too soon. If calculating by hand, always carry more decimal places within the calculations than is expected for the final result. If working with a calculator, carry the full value of the calculator entries until you arrive at the final result.
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While variance is a reliable method of spread, standard deviation (which is the square root of the variance) is a more popular method of spread. Standard deviation is also more "friendly" in that it has the same unit of measure as the original data.
Algebra 1 will concentrate on standard deviation.
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