Frequency Distributions (Page 3 of 3)

Other common distributions are U-shaped, J-shaped and reverse J-shaped (see below).


Where a group of data is not normally distributed, it is sometimes possible to transform the data such that is becomes normal (see the statistical guide, Transforming Data). This is 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. In the statistical guide, z-scores, we see the importance of the normal distribution and standard normal distribution in helping us to compare groups of data (for example, students' scores in a piece of English Literature coursework compared with a piece of Maths coursework) that have different means and standard deviations.

Standard Normal Distribution

When a frequency distribution is normally distributed (in other words, the group of data is symmetrically distributed around the middle of the scores) we can find out the probability of a score occurring by standardising the scores, known as standard scores (or z scores). For example, returning to our example of a tutor setting a piece of coursework for 100 students, we might want to know how likely it was (in other words, the probability) that a student scored more than 68 out of 100? The standard normal distribution simply converts the group of data in our frequency distribution such that the mean is 0 and the standard deviation is 1 (see below).



This provides us with a way of (a) understanding the probability of a score occurring and (b) comparing groups of data from distributions with different means and standard deviations. This is discussed in detail in the statistical guide, Standard Scores (z-scores).