## Statistics Tips (Part 4): Normality of Distribution

The Bell Curve (also known as the Gaussian Function/Distribution or Normality of Distribution) is a concept in mathematics and psychology. Basically, it refers to pattern that a given sample of data sometimes produces when it’s used to make a histogram (i.e. a graph that shows how frequently individual values/items occur). The pattern itself is shaped like a bell. The more common a value is then the closer it is to the peak or middle of the bell. The middle typically represents the average value.

Example

Most bell shapes you’ll come across in research reports aren’t completely perfect. The ideal normal distribution has the following characteristics:

• outliers are rare
• the mean, median and mode are equal
• 50% of values are less than the mean
• 50% of values are greater than the mean
• Approximately 68% of all values should be within one standard deviation of the mean
• Approximately 95.4% of all values should be within two standard deviations of the mean
• Approximately 99.8% of all values should be within three standard deviations of the mean

Example

The existence of a bell curve can be difficult to verify if the range of values you’re using is small or if the size of the sample you’re using is small. If you’re sample size is large enough you can often presume to have a normality of distribution because of what’s known as central limit theorem. The theorem purports that data is likely to have a normal distribution if it has a finite mean and variance and is produced from a large sample. A really good demonstration of these concepts is the computer programme ‘Quincunx’ which you can find at the following website: http://www.mathsisfun.com/data/quincunx.html

Summary: The bell curve (Gaussian function or normality of distribution) refers to a near symmetrical bell shaped pattern on a histogram of data frequencies where the more common a value the closer it is to the middle (average) of the pattern.