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The variance is a number that indicates how far a set of numbers lie apart. The variance is identical to the squared standard deviation and hence expresses “the same thing” (but more strongly).

Variance - Example

A study has 100 people perform a simple speed task during 80 trials. For each participant, 80 reaction times (in seconds) are thus recorded. Part of these data are shown below.

In studies like these, we typically see that people get faster as they perform the speed task more often.

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That is, the average reaction time tends to decrease over trials.
Also, reaction times will typically vary less between different people insofar as they perform the task more often. Technically, we say that the variance decreases over trials.

The table below illustrates this for trials 1,4,7 and 10.

Variance and Histogram

A great way to visualize the data from our previous table is a histogram for each trial. Like so, the figure below illustrates that participants got faster over trials; from trial 1 to trial 10 the histogram bars move leftwards, towards 0 se

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