Statistics · BEGINNER LESSON
Variance
Variance is a statistical measure of spread that describes how far values differ from their mean on average, using squared differences. Larger variance means the values are more spread out.
What it is
Variance is a summary statistic that measures spread, meaning how much data values differ from a central value such as the mean. In the sources, it is used to describe clinical variation and general data variation. Larger variance means greater spread among the values. [0,1]
[1] Table 2. [2] Advancing Methods to Study Clinical Variation in Healthcare - PMC
How it is computed
For a sample, first find the mean, then subtract the mean from each value, square each difference, add those squared differences, and divide by n − 1, where n is the number of data points. Squaring makes all terms positive, and the division gives the sample variance. [1]
[2] Advancing Methods to Study Clinical Variation in Healthcare - PMC
What it tells you
Variance shows how widely values are dispersed around the mean. A related measure, standard deviation, is the square root of variance, so it returns the spread to the original units. The coefficient of variation scales spread by dividing standard deviation by the mean. [0,1]
[1] Table 2. [2] Advancing Methods to Study Clinical Variation in Healthcare - PMC
Limits and caveats
Variance is limited to describing spread at the measurement level and does not explain why variation happens. The sources also note that common measures such as variance can be affected by sample size, because small samples may show extra random variation. Variance is also expressed in squared units, which can be less intuitive than the original data units. [0,1]
[1] Table 2. [2] Advancing Methods to Study Clinical Variation in Healthcare - PMC
SEE THE IDEA
How variance summarizes spread
The numbers or observations being studied.
The central value used as the reference point.
Each value minus the mean, then squared so negatives do not cancel positives.
The average of those squared differences, adjusted for sample size when using sample data.
Data values are compared with the mean; the squared differences are averaged to produce variance.
Variance is built from distances to the mean, but it uses squares rather than raw distances.
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Sources and further reading
This general lesson was generated from public source material. It explains a concept; it does not interpret a private paper or provide medical advice.