RLO: Descriptive statistics for interval and ratio scale data

Standard Deviation

The standard deviation explores the spread of scores, and it does this by giving a value (the standard deviation, or SD for short) which is calculated by looking at the differences between individual values and the mean. Thus, with a small SD we would known that a lot of values are close to the average value. Whereas, a large SD would indicate that values are generally further away from the average value.

For those of you with a mathematical bent then the standard deviation is calculated firstly squaring the difference between the individual value and the mean. We do this for all values, and add them together. This (large) number is then divided by one less than the number of individual scores. Finally we take the square root of this score to get the standard deviation. Sounds complex, but then it does tell us more about the spread of scores than a simple examination of the range might do. It is possible that we could have two data sets which have the same mean, mode, median, and range - so we might be tempted to think they are the same. It is only when we look at the SD do we find if this is the case or not.

One final point. When researchers report their data they often tell us the mean for their interval or ratio scale data, and alongside this (in brackets) they will tell us the SD.