**The Range**

The range is a simple measure of dispersion. You subtract the lowest score in the data set from the highest score to give the range. The range is a very simplistic measure and does not use all the scores in the data set therefore it can be distorted by a very high or low score that does not reflect the range of most of the other scores in between those two points.

**Standard deviation and when to use it**

- When you want to know how spread out a set of scores (data-points) are around the mean and the level of measurement is interval/ratio, the standard deviation is appropriate.

**How do you work it out?**

- In the exam booklet you will find the formula for standard deviation right at the beginning.
- The question might have a table for you to complete, if not then you should be very careful and lay out your workings neatly – you will lose marks unless you write out each stage accurately
- So first off remember X with a line over it means “the mean” for this set of data.
- So you need to start with the bit in brackets, neatly write out a column of figures where you calculate each score minus the mean, these are called d scores, d for deviation ,meaning how much does each score differ from the mean.
- Some of these scores will be negative, because the score is smaller then the mean, some will be positive, because the score was bigger than the mean
- To make all the d scores positive you need to square each of them, that is you need to calculate dxd and write it in the next column
- you then need to remind yourself that the sigma symbol means sum total, so add up all the d squared scores
- Now divide this number by the number of scores minus 1.
- So this gives you a figure called the variance, but we want the standard deviation so there is one last things to do, square root this figure to arrive at your destination, the standard deviation!!

## Strengths of the standard deviation

- When doing the calculation, we use every score and therefore is the most sensitive measure of central tendency telling us how ALL the data spread around the mean;
- for example the range only uses the highest and lowest scores and therefore we know little about the majority of the scores and how close they were to the mean
- if we want to use a parametric test (a set of more sensitive inferential stats tests, meaning that they help us to better avoid making type 1 and 2 errors) then we must have …
- homogeneity of variance, meaning that the standard deviation needs to be similar in each group
- normally distributed data (we need to know the standard deviation to work this out)

- if these criteria are not met then we must stick to a non-parametric test, e.g. Spearman’s, Wilcoxon’s , Mann Whitney, Chi Squared

## Weaknesses of using the standard deviation

- if there are any outliers, that is extreme scores which do not reflect the majority of the data, at either end (high or low) then the standard deviation can be affected
- standard deviation takes longer to calculate when done by hand