Measures of Dispersion (AQA A Level Psychology)

Measures of dispersion calculate the spread of scores and how much they vary in terms of how distant they are from the mean or median

• A data set with low dispersion will have scores that cluster around the measure of central tendency (the mean or median)

• A data set with high dispersion will have scores that are spread apart from the central measure with much variation among them

• If a data set contained exactly the same score per participant (e.g. everyone scored 15 out of 20 on a memory test) then the dispersion score would be zero as there would be no variation at all in the scores (plus the mean, mode and median would be identical = 15)

There are two measures of dispersion:

• The range

• Standard deviation 

The range describes the difference between the lowest and the highest scores in a data set

The range provides information as to the gap between the highest and lowest scores

To calculate the range subtract the lowest value from the highest value in the data set e.g.

• to calculate the range of 4, 4, 6, 7, 9, 9 subtract the lowest number (4) from the highest number (9)

• The range is 9

• When dealing with data that has been rounded +1 is added to the data set to account for any rounding up or down which has been applied to the original scores

  • 9 - 4 = 5 + 1 

  • Thus, the range = 6

The range provides a broad overview of the data which can be useful for some research purposes

The range is simple and easy to calculate

The range provides no information as to all of the other scores in the data set

• This means that it lacks validity as it does not indicate the degree of variation from the mean

The range is not very stable or representative

• It can vary from one sample to another as sample size increases

Standard deviation calculates how a set of scores deviates from the mean 

Standard deviation provides insight into how clustered or spread out the scores are from the mean

• A low standard deviation indicates that the scores are clustered tightly around the mean which indicates the reliability of the data set

• A high standard deviation indicates that the scores are more spread out from the mean which indicates lower reliability

Normal distributions have a low standard deviation as they reflect the fact that the scores are clustered close to the mean

There are six steps to calculating the standard deviation 

1. Calculate the mean 

2. Subtract the mean from each score in the data set

3. Square the scores which have just been calculated at step 2

4. Add all of the squared scores together 

5. Divide the total squared score by the number of scores minus 1

6. Work out the square root of the variance (using a calculator)

Standard deviation provides information as to how the scores are distributed across a data set

• This is a strength as it can indicate to what extent the data set is reliable and consistent

Standard deviation is more sensitive than the range as it uses all the scores in the data set 

• This means that it is a more valid representation of the data set

Standard deviation is onerous and time-consuming to calculate

• However, a statistical calculator or online tool can calculate the standard deviation much more quickly than in the past

Standard deviation can be skewed by extreme outliers

• these may inflate or depress the standard deviation, giving a misleading representation of the spread of values in the data set