They are less sensitive to a few extreme values than the range and show the spread of the 'typical' scores. The running total shows that 48 subjects in total took the test. The interquartile range will be the difference between the score of the 12th worst and the 36th worst and is shown by the green arrow. Variance and standard deviation Variance and standard deviation are the two most commonly used measures of variability. Variance is the mean squared deviation from the mean.
Standard deviation is a measure of the 'typical' distance from the mean.
Remember, from the lecture on averages, that deviations from the mean are both positive and negative, and that the sum of deviations from the mean is, by definition, always zero. Therefore, sum of deviations from the mean does not provide a measure of how well the mean describes the data. The proof is shown below. The mean has another important property. Squaring the errors is a mathematical trick to turn negative deviations into positive 'squared deviations'.