Measures of Dispersion (AQA A Level Psychology)
Revision Note
Range
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
Evaluation of the range
Strengths
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
Limitations
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
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
Calculate the mean
Subtract the mean from each score in the data set
Square the scores which have just been calculated at step 2
Add all of the squared scores together
Divide the total squared score by the number of scores minus 1
Work out the square root of the variance (using a calculator)
Evaluation of standard deviation
Strengths
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
Limitations
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
Worked Example
Here is an example of an A02 question you might be asked on this topic.
AO2: You need to apply your knowledge and understanding, usually referring to the ‘stem’ in order to do so (the stem is the example given before the question).
Professor Visage tested memory for faces as opposed to memory for names. Here are the mean scores and standard deviation per condition:
Condition | Mean /30 | Standard Deviation |
Names | 8.32 | 1.08 |
Faces | 10.75 | 3.64 |
Q. Comment on what the standard deviation reveals about the performance of participants per condition.
[3 marks]
Model answer:
Present your first point:
The standard deviation is higher in condition ‘Faces’ which indicates that there was more variability in performance in that condition, possibly due to faces being more complex than names to memorise. [1 mark]
Explain/expand on this point:
The fact that the mean for ‘Faces’ was higher shows that the dispersion of scores in this condition was wider than for ‘Names’ as it will have represented a range of higher and lower scores which is reflected in the higher mean. [1 mark]
Explain/expand the point further:
The ‘Names’ condition showed more clustering about the mean, thus less variability. [1 mark]
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