Frequency Distributions

Normal Distribution

If the group of data is symmetrically distributed around the middle of our scores, then the curve showing the distribution of scores will be bell-shaped. This is called the normal distribution (see below).



The shape of the curve tells us that (a) the majority of scores lie near to the centre of our distribution and (b) the frequency of scores decreases as we move away from the centre of our distribution. The normal distribution is extremely important because a wide range of statistical tests are based on the assumption that the group of data that they are examining is normally distributed (this is discussed further in many of the statistical guides on this website). Furthermore, many things that are studied in research, such as age, height, and so on, are normally distributed. Added to this, even a group of data this is not normally distributed can become normally distributed if a sufficient number of samples are taken (see the statistical guide, Sampling, for more information).

Other Common Types of Frequency Distribution

Not all frequency distributions are normally distributed. Some vary in their degree of pointyness (known as kurtosis) and others are not symmetrical (known as skewness). In terms of kurtosis, a pointy looking frequency distribution with a relatively thin tail is called a leptokurtic distribution whilst the opposite, a flat looking frequency distribution with a relatively heavy tailed distribution is called a platykurtic distribution (see below).


In terms of skewness, a frequency distribution is positively skewed if the centre of our distribution is at the lower end of our distribution with the tail pointing towards the higher (more positive) scores, whilst a frequency distribution is negatively skewed if the centre of our distribution is at the higher end of our distribution with the tail point towards the lower (more negative) scores.