Range and standard deviation

The range tells us the difference between the highest and lowest scores. It is the maximum value minus the minimum value plus one (to account for measurement error when rounding to whole numbers). This statistic is used with data that is at least ordinal (see below). If one child scores much higher or lower than the others (an outlier) then the range may seem very large, but really this does not tell us anything about the majority of the scores. If we have interval data we can use the standard deviation, which is the square root of the variance. Variance is a statistic which tells us about how the scores are spread around the mean. It involved calculating how much each score differs (deviates) from the mean and finding the average or standard amount of deviation. See figure 1 for the formula.

Figure 1: Formula to calculate standard deviation