Measures of dispersion | AQA A-Level Psychology Revision
- Revision Notes
- Aug 4
- 19 min read
Updated: 6 days ago
For 7182 specification, first teach in September 2025
AQA A-Level Psychology | Free Revision Notes
Estimated study time: 55 minutes
Measures of central tendency describe the typical score in a data set, but they do not reveal how much individual scores differ. This Measures of dispersion A-Level Psychology revision page explains how to calculate the range and standard deviation, interpret high and low values and select the most informative measure. AQA requires students to understand both measures, calculate the range and calculate standard deviation within psychological contexts.
Learning Objectives 🎯
By the end of this revision page, you should be able to:
Define dispersion, range and standard deviation.
Calculate the range accurately.
Explain what standard deviation measures.
Calculate standard deviation from a set of raw scores.
Interpret high, low and zero standard deviations.
Compare and evaluate the usefulness of the range and standard deviation.
Revision Notes 📚
What is dispersion?
Dispersion is the amount of variation or spread within a set of scores.
It shows how far individual scores differ from:
One another.
The centre of the distribution.
The mean score.
Two data sets can have the same measure of central tendency but very different levels of dispersion.
For example:
Group A scores | Group B scores |
8 | 2 |
9 | 6 |
10 | 10 |
11 | 14 |
12 | 18 |
Both groups have a mean of 10.
However:
Group A’s scores are closely clustered around 10.
Group B’s scores are spread much more widely.
A measure of central tendency alone would hide this important difference. This is why psychologists report dispersion alongside the typical or central value of a data set.
Why do psychologists measure dispersion?
Psychologists calculate dispersion to understand:
How similar participants’ scores are.
Whether scores cluster around the mean.
Whether there is substantial individual variation.
Whether one group is more variable than another.
Whether an average represents most participants accurately.
Whether an unusual or extreme score may be affecting the findings.
Measures of dispersion can be used with data from:
Experiments.
Questionnaires.
Observations.
Correlational studies.
Psychological tests.
Content analyses.
The AQA specification requires two measures of dispersion:
Range
Standard deviation
Measures of central tendency and dispersion
Measures of central tendency and dispersion answer different questions.
Type of measure | Question answered |
Central tendency | What is the typical or central score? |
Dispersion | How widely do the scores vary? |
A complete numerical description of a data set will often contain one measure of each.
For example:
The mean memory score was 14.6, with a standard deviation of 2.1.
This tells us:
The average score was 14.6.
Scores generally showed a relatively limited amount of variation around that average.
Without the standard deviation, the reader would not know whether most participants scored close to 14.6 or whether scores were spread widely.
The range
What is the range?
The range is the difference between the highest and lowest scores in a data set.
Range=highest score−lowest score
The range describes the total distance covered by the scores.
How to calculate the range
Use these steps:
Identify the highest score.
Identify the lowest score.
Subtract the lowest score from the highest score.
Include the correct unit where appropriate.
Worked example 1: memory scores
A psychologist records these memory scores:
6, 8, 9, 11, 14
The highest score is 14.
The lowest score is 6.
Range=14−6=8
The range is 8 points.
Worked example 2: response times
Participants complete a task in the following times:
22, 27, 25, 31, 24 seconds
The scores do not have to be placed in order, but doing so may make the calculation easier:
22, 24, 25, 27, 31
The highest time is 31 seconds.
The lowest time is 22 seconds.
Range=31−22=9
The range is 9 seconds.
Worked example 3: a negative lowest score
A psychologist records changes in questionnaire scores:
−4, −1, 0, 3, 6
The highest score is 6.
The lowest score is -4.
Range=6−(−4)
Subtracting a negative value is equivalent to addition:
6+4=10
The range is 10 points.
Calculating range from a frequency table
Consider this frequency table:
Score | Frequency |
2 | 3 |
3 | 5 |
4 | 4 |
5 | 2 |
7 | 1 |
The frequency does not change the calculation.
Highest recorded score = 7
Lowest recorded score = 2
Range=7−2=5
The range is 5.
Interpreting the range
A larger range indicates a greater total spread between the lowest and highest values.
A smaller range indicates that the most extreme values are closer together.
For example:
Condition | Lowest score | Highest score | Range |
Quiet | 12 | 18 | 6 |
Background noise | 5 | 20 | 15 |
The background-noise condition has the greater range.
This means that the distance between its lowest and highest scores is greater. It does not necessarily mean that every score in that condition is widely dispersed because the range considers only two values.
Strengths of the range
It is quick to calculate
Only the highest and lowest scores are needed.
This makes the range useful for:
A rapid summary.
Comparing the total spread of two groups.
Checking whether a data set contains a very wide set of values.
Estimating variation before carrying out further analysis.
It is easy to understand
A reader can see immediately how much distance separates the most extreme scores.
For example:
A range of 12 seconds means that the slowest response was 12 seconds longer than the fastest response.
It can help identify unusual scores
A surprisingly large range may encourage the researcher to examine whether:
An extreme score is present.
A participant misunderstood the task.
A recording error occurred.
The sample contains substantial genuine variation.
An unusual score should not automatically be removed, but it should be investigated.
Limitations of the range
It uses only two scores
The range depends entirely on:
The highest score.
The lowest score.
All the other scores are ignored.
For example, consider these data sets:
Data set A
1, 5, 5, 5, 9
Data set B
1, 2, 5, 8, 9
Both have the same range:
9−1=8
However:
Most scores in data set A cluster around 5.
Data set B is more widely distributed across the scale.
The range does not show this difference.
It is strongly affected by extreme scores
One unusually high or low score can increase the range substantially.
Consider:
4, 5, 5, 6, 7
The range is:
7−4=3
Now replace 7 with an extreme score of 30:
4, 5, 5, 6, 30
The range becomes:
30−4=26
Four of the five scores remain between 4 and 6, but the range increases from 3 to 26.
This may make the data appear more widely dispersed than most participants’ scores suggest.
It can vary greatly between samples
A different sample may contain a slightly higher or lower extreme score, changing the range even when the main pattern is similar.
The range may therefore be unstable, particularly with small samples.
It does not describe clustering
The range cannot tell us whether scores:
Cluster around the centre.
Are spread evenly.
Form separate groups.
Contain gaps.
Are concentrated at one end.
To understand these patterns, the researcher may also need a graph or distribution. These displays are covered in presenting quantitative results visually.
Standard deviation
What is standard deviation?
Standard deviation is a measure of how far scores typically deviate from the mean.
It considers the distance between:
Every score.
The mean score.
A standard deviation therefore uses all the values in the data set.
Interpreting standard deviation
A small standard deviation means that scores are generally clustered close to the mean.
A large standard deviation means that scores are generally spread further away from the mean.
A standard deviation of zero means that every score is identical.
Standard deviation | Meaning |
Small | Scores cluster closely around the mean |
Large | Scores are widely dispersed around the mean |
Zero | Every score has the same value |
A standard deviation cannot be negative.
Standard deviation and the mean
Standard deviation is calculated in relation to the mean.
Consider:
8, 9, 10, 11, 12
The mean is 10.
The scores are only a short distance from the mean:
8 is 2 below.
9 is 1 below.
10 is equal to the mean.
11 is 1 above.
12 is 2 above.
The standard deviation will therefore be relatively small.
Now consider:
2, 6, 10, 14, 18
The mean is also 10.
However, the scores are further from the mean:
2 is 8 below.
6 is 4 below.
10 is equal to the mean.
14 is 4 above.
18 is 8 above.
The standard deviation will be much larger, even though the two data sets have the same mean.
The standard deviation formula
For a complete set of scores, standard deviation may be calculated using:
Where:
σ= standard deviation
x = each individual score
x̄ = the mean
∑= add together
N = number of scores
The worked examples on this page treat the listed scores as the complete data set and divide by NNN. Where an examination question supplies a formula or specific instruction, follow the convention given in that question.
Why are the deviations squared?
Some scores lie above the mean and produce positive deviations.
Other scores lie below the mean and produce negative deviations.
If the deviations were simply added, the positive and negative values could cancel one another out.
For example, the deviations:
−2, −1, 0, +1, +2
add to zero.
Squaring the deviations makes them all positive:
4, 1, 0, 1, 4
This allows the total amount of variation to be calculated.
How to calculate standard deviation
Use the following steps:
Calculate the mean.
Subtract the mean from each score.
Square each deviation.
Add the squared deviations.
Divide by the number of scores.
Find the square root.
Round the final answer appropriately.
It is usually best to organise the calculation in a table.
Worked example: calculating standard deviation
A psychologist records these scores:
2, 4, 4, 4, 5, 5, 7, 9
Step 1: Calculate the mean
Add the scores:
2+4+4+4+5+5+7+9=40
There are eight scores:
x̄=40÷8=5
The mean is 5.
Step 2: Calculate each deviation from the mean
Subtract 5 from each score.
Step 3: Square each deviation
Score x | x−x̄ | (x−x̄)² |
2 | -3 | 9 |
4 | -1 | 1 |
4 | -1 | 1 |
4 | -1 | 1 |
5 | 0 | 0 |
5 | 0 | 0 |
7 | 2 | 4 |
9 | 4 | 16 |
Total | 32 |
Step 4: Divide by the number of scores
32÷8=4
Step 5: Find the square root
√4=2
The standard deviation is:
2
Interpreting the answer
The standard deviation of 2 indicates that scores generally show a spread of approximately two points around the mean of 5.
It does not mean that every score is exactly two points from the mean. Standard deviation summarises the overall pattern of deviation.
Worked example: a decimal standard deviation
A psychologist records the scores:
3, 4, 5, 6, 7
Step 1: Calculate the mean
x̄=(3+4+5+6+7)÷5=5
Step 2: Calculate and square the deviations
Score | Deviation from 5 | Squared deviation |
3 | -2 | 4 |
4 | -1 | 1 |
5 | 0 | 0 |
6 | 1 | 1 |
7 | 2 | 4 |
Total | 10 |
Step 3: Divide by N
10÷5=2
Step 4: Find the square root
√2=1.4142…
Rounded to two decimal places:
1.41
The standard deviation is 1.41 points.
Rounding standard deviation
Unless instructed otherwise:
Keep full calculator values during intermediate stages.
Round only the final answer.
Use a sensible number of decimal places.
Include units where appropriate.
Premature rounding may slightly change the final answer.
The use of appropriate decimal places and significant figures is developed in working accurately with numerical data.
Calculating standard deviation from a frequency table
A frequency table shows how many times each score occurs.
Consider:
Score x | Frequency f |
1 | 1 |
2 | 2 |
3 | 1 |
The complete data set is:
1, 2, 2, 3
Step 1: Calculate the mean
x̄=(1+2+2+3)÷4=2
Step 2: Calculate squared deviations and include frequency
Score x | Frequency f | (x−x̄)² | f(x−x̄)² |
1 | 1 | 1 | 1 |
2 | 2 | 0 | 0 |
3 | 1 | 1 | 1 |
Total | 4 | 2 |
Step 3: Divide by the total frequency
2÷4=0.5
Step 4: Find the square root
√0.5=0.7071…
Rounded to two decimal places:
0.71
The standard deviation is 0.71.
Using a calculator to find standard deviation
A scientific calculator may calculate standard deviation through its statistical mode.
The exact buttons depend on the calculator, but the general process is:
Enter statistical or data mode.
Select one-variable statistics.
Enter every score.
Check that repeated scores are included.
Request the standard-deviation value.
Select the convention required by the question.
Round the answer only at the end.
Even when using a calculator, you should understand:
What standard deviation measures.
What the final number means.
Why two groups may have different values.
How an outlier may affect the result.
Always check that the answer is plausible. A typing error can produce a calculator result that looks precise but is incorrect.
Comparing groups using standard deviation
Consider the following results:
Condition | Mean score | Standard deviation |
Quiet | 18.4 | 1.6 |
Background noise | 18.2 | 5.7 |
The means are very similar.
However:
Scores in the quiet condition cluster relatively closely around 18.4.
Scores in the background-noise condition are much more widely dispersed around 18.2.
This suggests that participant performance was more variable in the background-noise condition.
It does not explain why the variation occurred. Possible explanations might include:
Participant differences.
Inconsistent reactions to noise.
Procedural differences.
Measurement error.
Genuine individual variation.
Standard deviation and consistency
A smaller standard deviation means that scores are more tightly clustered.
It does not automatically show that:
The study is reliable.
The measure is valid.
The procedure was well controlled.
One condition is better.
The findings are statistically significant.
A low standard deviation describes the pattern of scores. Reliability is a separate research-methods concept concerning the consistency of a procedure or measure.
Standard deviation of zero
Consider:
6, 6, 6, 6, 6
The mean is 6.
Every score has a deviation of zero:
6−6=0
Every squared deviation is also zero.
Therefore:
σ=0
A standard deviation of zero means there is no variation in the data set.
It does not necessarily mean that the measure is valid or that the investigation is scientifically strong. It shows only that every recorded value was the same.
Standard deviation and extreme scores
Standard deviation uses every score, so it is affected by extreme values.
Consider:
4, 5, 5, 6, 7
Most scores cluster around 5 or 6.
If 7 is replaced with 30:
4, 5, 5, 6, 30
The extreme value:
Increases the mean.
Produces a large deviation from the mean.
Produces an even larger squared deviation.
Increases the standard deviation.
Standard deviation is therefore not resistant to outliers.
However, it generally provides more information than the range because it uses every score rather than only the two extremes.
Why standard deviation may be preferable when there is an outlier
An outlier can dominate the range completely because the range is based only on the highest and lowest scores.
Standard deviation is also affected, but it shows the outlier’s influence as part of the complete pattern of scores.
A researcher can compare:
The mean.
The standard deviation.
The range.
A graph of the distribution.
Together, these reveal whether the large spread reflects many dispersed scores or one isolated value.
Comparing range and standard deviation
Feature | Range | Standard deviation |
What it measures | Distance between the highest and lowest scores | Typical spread of scores around the mean |
Scores used | Only the highest and lowest | Every score |
Calculation | Highest minus lowest | Uses deviations from the mean |
Difficulty | Quick and simple | More complex |
Effect of extreme scores | Strongly affected | Also affected, especially because deviations are squared |
Detail provided | Limited | More complete |
Main advantage | Fast overview of total spread | Uses all the information in the data set |
Main limitation | Ignores most scores | Requires more calculation and an appropriate numerical scale |
Strengths of standard deviation
It uses every score
Each score contributes to the calculation.
This provides a more complete measure of variation than the range.
It measures spread around the mean
Standard deviation directly shows how tightly scores cluster around the average.
This helps researchers judge whether the mean represents most participants well.
It distinguishes distributions with the same range
Consider:
Data set A
1, 5, 5, 5, 9
Data set B
1, 2, 5, 8, 9
Both have:
Mean = 5
Range = 8
However, data set B has more scores located away from the mean.
Its standard deviation is therefore larger.
Standard deviation reveals a difference that the range misses.
It allows more detailed comparisons
Researchers can compare:
Two conditions with similar means.
Groups with the same range.
Scores collected on two occasions.
Variability across different samples.
It is useful in further statistical analysis
Standard deviation contributes to other statistical procedures and helps describe the shape and spread of numerical distributions.
Limitations of standard deviation
It is more difficult to calculate
The procedure involves:
Calculating the mean.
Finding deviations.
Squaring values.
Adding them.
Dividing.
Finding a square root.
This creates more opportunities for arithmetic or data-entry errors.
It is affected by extreme scores
Large deviations are squared, so extreme values can influence standard deviation substantially.
Researchers should inspect the original data rather than interpreting the standard deviation in isolation.
It depends on the mean
Standard deviation is calculated around the mean. It is therefore most appropriate when the mean is a meaningful measure of central tendency.
Where the median is preferred because data are ordinal or strongly skewed, standard deviation may not be the most suitable description of dispersion.
It may conceal the exact distribution
Two data sets can have similar means and standard deviations but differ in:
Shape.
Clusters.
Gaps.
Number of peaks.
Presence of unusual values.
A graph may therefore be needed alongside the numerical summary.
Range and standard deviation applied to the same data
Consider the scores:
8, 9, 10, 11, 12
Range
12−8=4
Standard deviation
The mean is 10.
Score | Deviation | Squared deviation |
8 | -2 | 4 |
9 | -1 | 1 |
10 | 0 | 0 |
11 | 1 | 1 |
12 | 2 | 4 |
Total | 10 |
σ=√(10÷5)
σ=√2=1.41
The scores cover a total distance of 4 points and typically vary by approximately 1.41 points around the mean.
Selecting a measure of dispersion
The appropriate measure depends on:
The level of measurement.
The selected measure of central tendency.
The distribution of scores.
The presence of extreme values.
The amount of detail required.
When the range may be appropriate
The range may be selected when:
A quick measure is required.
The researcher wants to report the total spread.
The calculation must be simple.
The data set is small.
The highest and lowest scores are of particular interest.
A justification might be:
The range provides a quick comparison of the total spread of scores in the two conditions.
When standard deviation may be appropriate
Standard deviation may be selected when:
The data are numerical.
The mean has been calculated.
All scores should contribute.
Researchers want to compare clustering around the mean.
A more detailed measure of dispersion is required.
A justification might be:
Standard deviation is more appropriate because it uses every participant’s score and shows how widely the scores are spread around the mean.
Range with the median
Where the median is used, the range may provide a simple accompanying measure.
However, researchers should still consider whether an extreme value is distorting the range.
Standard deviation with the mean
The mean and standard deviation are often reported together because:
Both use every numerical score.
Standard deviation describes spread around the mean.
Together they provide a summary of centre and variation.
The level of measurement should still be checked. This is developed in nominal, ordinal and interval data.
Dispersion and distributions
The same measure of dispersion may be interpreted differently depending on the shape of the distribution.
Researchers should consider whether the scores are:
Normally distributed.
Positively skewed.
Negatively skewed.
Bimodal.
Affected by an outlier.
In a skewed distribution, the mean and standard deviation may be strongly influenced by scores in the tail.
The median may provide a more representative centre, but the range may still be dominated by the most extreme value.
These patterns are explored further in normal and skewed patterns of scores.
Dispersion and research conclusions
A researcher should avoid drawing conclusions from dispersion alone.
For example, a larger standard deviation does not show that:
The independent variable caused greater variation.
The condition was less reliable.
The group performed worse.
The difference is statistically significant.
The study lacked validity.
Dispersion describes the sample’s scores.
A complete conclusion may also need:
The mean or median.
The research design.
A graph.
An inferential test.
Consideration of alternative explanations.
Dispersion in psychological investigations
Experiments
Researchers may calculate:
The range of dependent-variable scores.
The standard deviation for each condition.
This allows comparison of both average performance and participant variation.
Questionnaires
Researchers may examine:
The range of numerical ratings.
The standard deviation of total questionnaire scores.
A wide spread might indicate substantial differences in participants’ responses.
However, researchers should still check whether the questionnaire has been scored validly.
Observations
Where behaviour is recorded numerically, researchers may calculate:
The range of behavioural frequencies.
The standard deviation of frequencies across participants or observation periods.
For example, the number of interruptions may vary greatly between participants.
Correlational studies
Researchers may report dispersion for each co-variable.
For example:
Mean and standard deviation of sleep duration.
Mean and standard deviation of concentration scores.
The correlation coefficient then describes the relationship between the two variables rather than their separate spread.
Psychological reports
Measures of dispersion normally appear in the results section.
For example:
Participants in the quiet condition achieved a mean score of 16.8, with a standard deviation of 2.3.
The discussion section may then interpret the difference in variability and consider possible explanations.
This follows the structure covered in communicating the findings of an investigation.
Measures of dispersion A-Level Psychology revision: exam technique
Questions may ask you to:
Calculate a range.
Calculate a standard deviation.
Interpret a standard deviation.
Compare two standard deviations.
Explain why standard deviation is preferable to range.
Explain how an extreme score affects dispersion.
Identify which group has more variable scores.
Answering a range calculation
Show the subtraction:
Range=18−6=12
Do not write only the final value where working marks may be available.
Answering a standard-deviation comparison
Weak answer:
Group B has a larger standard deviation.
Stronger answer:
Group B has the larger standard deviation, so its scores are more widely dispersed around the mean than the scores in Group A.
Explaining why standard deviation is more useful
Weak answer:
Standard deviation is more accurate.
Stronger answer:
Standard deviation uses every score and measures spread around the mean, whereas the range uses only the highest and lowest scores. It therefore provides a more complete description of variation.
Applying an extreme score
Weak answer:
The outlier changes the dispersion.
Stronger answer:
The unusually high score becomes the maximum value, so it substantially increases the range. It also increases the standard deviation because its distance from the mean is large and that deviation is squared during the calculation.
Comparing two groups fully
A good comparison should refer to:
The measure of central tendency.
The measure of dispersion.
The direction of the difference.
What the numbers suggest about participant scores.
For example:
Both conditions have a mean score of 12, but Condition B has a standard deviation of 5.1 compared with 1.4 in Condition A. Participants therefore achieved similar average scores, but performance was much more variable in Condition B.
Checking calculations
Before submitting an answer, check:
For the range
Have you identified the actual highest score?
Have you identified the actual lowest score?
Have you subtracted lowest from highest?
Have you handled negative values correctly?
Have you included the unit?
For standard deviation
Have you calculated the mean correctly?
Have you included every score?
Have you calculated each deviation from the mean?
Have you squared each deviation?
Have you added the squared deviations correctly?
Have you divided by the correct number?
Have you found the square root?
Have you rounded only the final answer?
Is the answer non-negative?
Is the answer plausible given the spread of scores?
Key Words 🔑
Key word | Student-friendly definition | How it may be used in an exam |
Dispersion | The amount of variation or spread within a data set. | Explain why a measure of central tendency gives an incomplete description. |
Range | The difference between the highest and lowest scores. | Calculate the total spread of a set of values. |
Standard deviation | A measure of how far scores typically vary from the mean. | Compare the spread of scores in two conditions. |
Mean | The total of all scores divided by the number of scores. | Calculate the centre around which standard deviation is measured. |
Deviation | The difference between an individual score and the mean. | Complete the stages of a standard-deviation calculation. |
Squared deviation | A deviation multiplied by itself. | Prevent positive and negative deviations from cancelling. |
Extreme score | A value much higher or lower than most of the other scores. | Explain why the range or standard deviation has increased. |
Outlier | An unusual score that lies a considerable distance from the main group of values. | Evaluate whether a measure of dispersion represents most participants. |
Variation | Differences among scores within a data set. | Interpret a high or low standard deviation. |
Clustering | Scores being grouped closely around a central value. | Explain what a small standard deviation indicates. |
Descriptive statistics | Numerical methods used to organise and summarise data. | Classify range and standard deviation. |
Measure of central tendency | A statistic representing the centre or typical value of a data set. | Explain why the mean and standard deviation are often reported together. |
Distribution | The overall pattern formed by scores in a data set. | Explain why a graph may be required alongside numerical statistics. |
Frequency | The number of times a score occurs. | Calculate standard deviation from a frequency table. |
Variance | The mean of the squared deviations before the square root is calculated. | Identify the stage immediately before obtaining standard deviation. |
Common Mistakes ⚠️
Mistake: Adding the highest and lowest scores when calculating the range.
Why this is incorrect:The range is the difference between the extreme scores.
How to improve:Use:
highest score−lowest score
Mistake: Counting the number of scores between the minimum and maximum.
Why this is incorrect:The range concerns the numerical distance between the scores, not the number of observations.
How to improve:Subtract the lowest value from the highest value.
Mistake: Ignoring a negative sign when calculating the range.
Why this is incorrect:Subtracting a negative value increases the result.
How to improve:Write the calculation fully, such as:
6−(−4)=10
Mistake: Defining standard deviation as the distance between the highest and lowest scores.
Why this is incorrect:This describes the range.
How to improve:State that standard deviation measures how far scores typically vary around the mean.
Mistake: Saying that a larger standard deviation means a higher average.
Why this is incorrect:Standard deviation describes spread, not central tendency.
How to improve:Interpret the mean and standard deviation separately.
Mistake: Assuming that a small standard deviation proves reliability.
Why this is incorrect:A small standard deviation shows that scores cluster closely. It does not show that the measure would produce consistent results on another occasion.
How to improve:Use standard deviation to describe variation and evaluate reliability separately.
Mistake: Forgetting to square negative deviations.
Why this is incorrect:Both positive and negative deviations become positive when squared.
How to improve:Use brackets when entering negative values:
(−3)²=9
Mistake: Adding deviations before squaring them.
Why this is incorrect:Positive and negative deviations from the mean will usually cancel.
How to improve:Square each individual deviation before adding them.
Mistake: Forgetting the square root at the end of the calculation.
Why this is incorrect:The value before the square root is not the standard deviation.
How to improve:Check that the final step returns the measure to the original unit of the data.
Mistake: Rounding at every stage.
Why this is incorrect:Repeated rounding can alter the final answer.
How to improve:Keep full calculator values and round only the final standard deviation.
Mistake: Claiming that standard deviation is unaffected by extreme scores.
Why this is incorrect:An extreme score has a large deviation from the mean, and this deviation is squared.
How to improve:Explain that both range and standard deviation are affected, although standard deviation uses every score.
Mistake: Claiming that standard deviation is always better than range.
Why this is incorrect:The range may be suitable when a quick summary of the total spread is required.
How to improve:Select the measure according to the data and research purpose.
Mistake: Comparing standard deviations without explaining them.
Why this is incorrect:Simply identifying the larger value does not interpret what it means.
How to improve:State that the larger value indicates greater dispersion around the mean.
Exam-Style Questions ✍️
Question 1
Define dispersion. (2 marks)
Question 2
A psychologist records the following memory scores:
6, 9, 12, 8, 15, 11
Calculate the range. Show your working. (2 marks)
Question 3
Participants complete a task in the following times:
−2, 1, 3, 5, 8
Calculate the range. (2 marks)
Question 4
Explain what is meant by standard deviation. (2 marks)
Question 5
Group A has a standard deviation of 1.8 and Group B has a standard deviation of 6.4.
Explain what these values suggest about the scores in the two groups. (3 marks)
Question 6
A psychologist records these scores:
3, 4, 5, 6, 7
Calculate the standard deviation. Show each stage of your working and give your answer to two decimal places. (6 marks)
Question 7
The results of two conditions are shown below.
Condition | Mean | Range | Standard deviation |
Quiet | 14.2 | 5 | 1.3 |
Noise | 14.0 | 17 | 5.8 |
Compare the performance of participants in the two conditions. (4 marks)
Question 8
A data set contains one score that is much higher than all the others.
Explain how this score may affect:
The range
The standard deviation
(4 marks)
Question 9
Explain one strength and one limitation of the range as a measure of dispersion. (4 marks)
Question 10
Compare the range and standard deviation as measures of dispersion. In your answer, refer to:
How each measure is calculated
The scores used
The effect of extreme scores
The amount of information provided
Their usefulness when comparing psychological data
(8 marks)
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