Normal distribution

Data that is normally distributed produces a symmetrical bell‐shaped curve when plotted, indicating that most scores are close to the mean, with a progressively fewer scores being located at the extremes of either tail of the distribution. In this instance, the median and mode also occupy the same centre point of the curve as the mean does.

For any data set to be considered normally distributed 68.26% will lie within one standard deviation of the mean (34.13% either side) and 94.55% of scores will lie within two standard deviations from the mean. As a result, only 4.56% of scores will lie beyond two standard deviations from the mean (2.28% above or below).

Skewed distribution

Sometimes data does not follow this symmetrical pattern which can result in a large proportion of scores falling below the mean (positively skewed) or after the mean (negatively skewed).

In both instances, the mode remains at the highest point on the graph, since it is not affected by extreme scores.