Measures of central tendency | AQA A-Level Psychology Revision

For 7182 specification, first teach in September 2025

AQA A-Level Psychology | Free Revision Notes

Estimated study time: 55 minutes

Psychologists often collect many scores, so they need a clear way to describe the typical or central value within a data set. This Measures of central tendency A-Level Psychology revision page explains how to calculate the mean, median and mode, select the most appropriate measure and assess the effect of extreme scores. These descriptive statistics help researchers summarise quantitative findings, compare conditions and communicate patterns clearly. Choosing the correct measure depends on the level of measurement, the distribution of scores and the purpose of the investigation.

Learning Objectives 🎯

By the end of this revision page, you should be able to:

• Define the mean, median and mode.

• Calculate each measure of central tendency accurately.

• Calculate measures of central tendency from raw scores and frequency tables.

• Select and justify an appropriate measure for a given data set.

• Explain how extreme scores affect the mean, median and mode.

• Interpret measures of central tendency within psychological investigations.

Revision Notes 📚

What are descriptive statistics?

Descriptive statistics are numerical techniques used to organise, summarise and present data.

They help researchers describe:

• The typical score.

• The spread of scores.

• Differences between conditions.

• Patterns within a data set.

• Relationships between variables.

Measures of central tendency are one type of descriptive statistic. Measures of dispersion provide additional information about how widely scores vary.

The scores being summarised will usually be numerical information collected during an investigation.

What is central tendency?

Central tendency refers to the typical, central or representative value within a set of scores.

There are three measures of central tendency required for AQA A-Level Psychology:

1. Mean

2. Median

3. Mode

Each measure identifies the centre of the data in a different way.

Measure	How the central value is identified
Mean	Adds all scores and divides by the number of scores
Median	Finds the middle score after placing the data in order
Mode	Identifies the most frequently occurring score or category

The three measures can produce the same value, but they do not always do so.

Why do psychologists calculate central tendency?

Imagine that a psychologist records the memory scores of 50 participants.

Listing all 50 scores would make it difficult to understand the overall pattern. A measure of central tendency reduces the data to one value that represents the centre of the group.

Psychologists may use measures of central tendency to:

• Summarise participant performance.

• Compare experimental conditions.

• Compare different groups.

• Describe questionnaire ratings.

• Report observational frequencies.

• Present the central value in a table or graph.

For example, a researcher may compare:

• The mean recall score in a silent condition.

• The mean recall score in a background-noise condition.

However, one central value cannot show every feature of the data. Researchers should usually consider it alongside the amount of variation between scores.

The mean

What is the mean?

The mean is calculated by adding all the scores and dividing the total by the number of scores.

The mean uses every value in the data set.

How to calculate the mean

Use the following steps:

1. Add all the scores.

2. Count how many scores there are.

3. Divide the total by the number of scores.

4. Include an appropriate level of precision in the answer.

Worked example 1: calculating a whole-number mean

A psychologist records the following memory scores:

4, 6, 7, 8, 10

Step 1: Add the scores

4+6+7+8+10=35

Step 2: Count the scores

There are five scores.

Step 3: Divide

Mean=35÷5=7

The mean memory score is 7.

Worked example 2: calculating a decimal mean

A researcher records the following number of correct responses:

3, 4, 6, 6, 8

Add the scores:

3+4+6+6+8=27

Divide by the number of scores:

Mean=27÷5=5.4

The mean number of correct responses is 5.4.

A mean does not have to be one of the original scores.

Worked example 3: mean response time

Five participants complete a task in:

42, 38, 51, 45, 39 seconds

Add the response times:

42+38+51+45+39=215

Divide by five:

Mean=215÷5=43

The mean response time is 43 seconds.

Always include the unit where one is provided.

Calculating the mean from a frequency table

A frequency table shows how many times each score occurred.

Test score	Frequency
2	1
3	2
4	3
5	2

To calculate the mean:

1. Multiply each score by its frequency.

2. Add the products.

3. Add the frequencies.

4. Divide the total of the products by the total frequency.

Score xxx	Frequency fff	x×fx \times fx×f
2	1	2
3	2	6
4	3	12
5	2	10
Total	8	30

Mean=30÷8=3.75

The mean test score is 3.75.

Why is the mean useful?

It uses every score

Every value contributes to the calculation. This means the mean represents the entire data set rather than only one or two values.

It distinguishes between similar data sets

The mean is sensitive to differences between scores.

Consider these data sets:

• Data set A: 2, 4, 6

• Data set B: 3, 4, 5

Both have a median of 4 and a mode does not exist. Their means are also both 4 in this example, but in many similar data sets the mean will reveal differences not shown by the median or mode.

It is useful for further calculations

The mean is used in other statistical procedures, including the calculation of standard deviation.

It provides a precise summary

The mean may produce a decimal value, allowing relatively small differences between conditions to be identified.

Limitations of the mean

It is affected by extreme scores

A very high or very low value changes the total and can pull the mean away from most of the scores.

It may not be an observed score

The calculated mean may be a value that no participant actually obtained.

For example, the mean number of children in a family could be 1.8, although no family has 1.8 children.

It is not appropriate for every level of measurement

The mean requires numerical values for which the differences between scores are meaningful. It should not be calculated for nominal categories.

It may give a misleading impression in a skewed distribution

When most scores cluster at one end and a small number extend into a tail, the mean can be pulled towards the tail.

These patterns are explored in normal and skewed distributions.

The median

What is the median?

The median is the middle score when the data are arranged in numerical order.

The median divides an ordered set of scores into two halves:

• Half the scores lie at or below the median.

• Half the scores lie at or above the median.

The scores must be placed in order before the median is identified.

Calculating the median with an odd number of scores

Consider the scores:

9, 3, 7, 5, 6

Step 1: Put the scores in order

3, 5, 6, 7, 9

Step 2: Identify the middle score

There are five scores, so the third score is in the middle.

The median is 6.

Finding the median position

For an odd number of scores, the position of the median can be found using:

where n is the number of scores.

For five scores:

(5+1)÷2=3

The median is therefore the third score in the ordered data set.

Calculating the median with an even number of scores

Consider the scores:

2, 4, 5, 8, 9, 12

There are six scores, so there is no single middle score.

The two middle scores are the third and fourth values:

5 and 85\text{ and }85 and 8

Calculate the midpoint:

Median=(5+8)÷2=6.5

The median is 6.5.

Another even-number example

Scores:

3, 4, 6, 6, 9, 11, 12, 15

The middle scores are the fourth and fifth values:

6 and 9

Median=(6+9)÷2=7.5

The median is 7.5.

The median does not have to be an observed score.

Calculating the median from a frequency table

Consider the following data:

Score	Frequency
1	2
2	3
3	4
4	1

There are:

2+3+4+1=10

scores in total.

Because there are ten scores, the median lies between the fifth and sixth scores.

Expand the frequency information mentally:

1, 1, 2, 2, 2, 3, 3, 3, 3, 4

The fifth score is 2 and the sixth is 3.

Median=(2+3)÷2=2.5

The median is 2.5.

Why is the median useful?

It is less affected by extreme scores

The median depends on the position of scores rather than their exact numerical size.

A very high score may have little or no effect on the median if it remains at the end of the ordered data set.

It is useful with skewed data

When a distribution contains a long tail or extreme values, the median may represent the typical participant more accurately than the mean.

It can be used with ordinal data

The median requires scores or categories to be placed in order. It does not require the intervals between values to be equal.

This makes it suitable for some forms of ranked or ordinal data.

Limitations of the median

It does not use the exact value of every score

The median is determined mainly by the central position. Changes to scores at either end may not affect it.

It may ignore meaningful differences

Two data sets can have the same median even though their scores differ considerably.

For example:

• Data set A: 1, 2, 3, 4, 5

• Data set B: 1, 1, 3, 20, 50

Both have a median of 3, but their distributions are very different.

It requires ordered data

The median cannot be calculated for categories that have no meaningful order.

The mode

What is the mode?

The mode is the most frequently occurring score or category.

Unlike the mean and median, the mode can be used with non-numerical categories.

Calculating the mode

Consider the following scores:

2, 3, 3, 4, 5, 5, 5, 7

The score 5 occurs three times, more often than any other value.

The mode is 5.

Mode with categorical data

A psychologist asks participants which revision resource they use most frequently.

Revision resource	Number of participants
Flashcards	12
Textbook	7
Practice questions	18
Videos	9

The modal category is practice questions because it was selected by the largest number of participants.

This is one reason the mode is suitable for nominal data.

A data set with no mode

Consider:

2, 3, 4, 5, 6

Every score occurs once.

There is no mode.

Do not state that every score is the mode. The data set has no value that occurs more frequently than the others.

A data set with two modes

Consider:

2, 2, 3, 4, 4, 5

Both 2 and 4 occur twice.

The data set is bimodal, with modes of 2 and 4.

A data set may also have more than two modes if several values share the highest frequency.

Why is the mode useful?

It can be used with nominal data

The mode is the only measure of central tendency that can identify the most common unordered category.

For example, it could identify the most common:

• Sampling method selected by students.

• Revision resource used.

• Experimental condition preference.

• Type of observed behaviour.

It is quick to identify

The most frequent value may be visible immediately from a list, frequency table or bar chart.

It represents an actual score or category

Unlike the mean or an even-number median, the mode must be a value or category that occurred in the data.

It is not usually changed by one extreme score

An isolated high or low value normally does not alter which score occurs most often.

Limitations of the mode

There may be no mode

If every score occurs equally often, the measure cannot identify one typical value.

There may be several modes

A bimodal or multimodal data set does not produce one clear central score.

It does not use every score

The mode considers only frequency. It ignores the exact values and positions of the other scores.

It may not represent most participants well

The modal score may occur only slightly more often than other values.

For example:

2, 3, 4, 4, 5, 6, 7

The mode is 4, but it was obtained by only two of seven participants.

Comparing the mean, median and mode

Feature	Mean	Median	Mode
Definition	Arithmetic average	Middle ordered score	Most frequent score or category
Uses every exact score	Yes	No	No
Requires data to be ordered	No	Yes	No
Affected by extreme scores	Strongly	Usually less affected	Usually unaffected unless frequencies change
Can be used with nominal data	No	No	Yes
Can be used with ordinal data	Usually not preferred	Yes	Yes
Can be used with interval data	Yes	Yes	Yes
May not be an observed score	Yes	Yes, with even data	No
Can have more than one answer	No	No	Yes
May not exist	No	No	Yes

Selecting an appropriate measure of central tendency

The most appropriate measure depends on:

1. The level of measurement.

2. Whether the distribution contains extreme scores.

3. Whether the data are skewed.

4. Whether every score should contribute to the calculation.

5. The purpose of the analysis.

Selection based on level of measurement

The AQA specification requires knowledge of nominal, ordinal and interval levels of measurement. These are covered fully in nominal, ordinal and interval data.

A useful selection guide is:

Level of measurement	Appropriate measures
Nominal	Mode
Ordinal	Median or mode
Interval	Mean, median or mode, depending on the distribution

Nominal data

Nominal data consist of categories without a meaningful numerical order.

Examples include:

• Type of revision resource.

• Category of observed behaviour.

• Chosen experimental condition.

• Preferred response option where the options are unordered.

The mode is appropriate because researchers can identify the most frequently occurring category.

The mean cannot be calculated because the categories do not have meaningful numerical values.

The median cannot be identified because the categories cannot be placed in a meaningful rank order.

Ordinal data

Ordinal data can be placed in rank order, but the intervals between positions are not necessarily equal.

Examples include:

• Rankings.

• Ordered rating categories.

• Positions in a competition.

• Responses ranging from strongly disagree to strongly agree.

The median may be appropriate because it identifies the middle position without assuming equal intervals.

The mode may also be used to identify the most common rank or category.

The mean is generally avoided because the numerical gaps between ranks may not represent equal differences.

Interval data

Interval data use numerical measurements with meaningful, equal units.

Examples may include:

• Time in seconds.

• Number of correct answers.

• Test scores where numerical differences are meaningful.

• Number of behaviours observed.

The mean is often suitable because it uses all the numerical information.

However, the median may be more representative if the distribution contains extreme scores or is strongly skewed.

The mode may be reported, but it usually uses less information than the mean.

Selection based on extreme scores

When interval data contain no problematic extreme values, the mean is often the most informative measure because it uses every score.

When one or more extreme scores distort the average, the median may be more representative.

For example, consider the following completion times:

20, 21, 21, 22, 76

The mean is:

20+21+21+22+76÷5

=160÷5

=32

The median is 21.

A completion time of 32 seconds does not represent most participants well. Four of the five participants completed the task in 20 to 22 seconds.

The median of 21 is therefore likely to be a more representative measure of central tendency.

Selection based on skewed data

A skewed distribution contains a tail of scores extending towards higher or lower values.

Extreme scores in the tail pull the mean in their direction.

In a skewed distribution:

• The mean is affected by the tail.

• The median is usually less affected.

• The mode remains at the most frequent point.

The median may therefore provide a better description of the typical score.

Selection when every score matters

The mean is often preferred when:

• The data are interval.

• The distribution is reasonably balanced.

• There are no highly influential extreme scores.

• Researchers want every score to contribute.

• Further statistical analysis will use the mean.

Selection when the most common response matters

The mode is useful when the research question concerns popularity or frequency.

For example:

Which revision technique was selected most frequently?

The mode answers this question directly.

Calculating an arithmetic average would not be meaningful.

Selection when the middle rank matters

The median is useful when:

• Data are ordered.

• The intervals between scores are uncertain.

• Extreme scores are present.

• The researcher wants the central position.

For example, the median ranking could describe the central position in a set of ordered ratings.

Extreme scores

What is an extreme score?

An extreme score is a value that is much higher or lower than most of the other scores in the data set.

It may occur because:

• One participant genuinely performed very differently.

• The participant misunderstood the task.

• The researcher recorded the score incorrectly.

• Equipment malfunctioned.

• The sample naturally contains considerable variation.

Researchers should not remove an extreme score merely because it is inconvenient. They should investigate its origin and apply justified procedures consistently.

How extreme scores affect the mean

The mean uses the numerical value of every score.

An extreme value changes the total substantially and therefore pulls the mean towards it.

Consider:

4, 5, 5, 6, 7

The mean is:

27÷5=5.4

Now replace the score of 7 with an extreme score of 30:

4, 5, 5, 6, 30

The mean becomes:

50÷5=10

The extreme score raises the mean from 5.4 to 10, even though four of the five scores remain between 4 and 6.

This makes the mean less representative of the majority of participants.

How extreme scores affect the median

For the scores:

4, 5, 5, 6, 7

the median is 5.

After replacing 7 with 30:

4, 5, 5, 6, 30

the median remains 5.

The exact size of the highest score does not affect the middle position.

An extreme score can affect the median if it changes the order or central positions, but the median is usually much less sensitive than the mean.

How extreme scores affect the mode

For both data sets:

4, 5, 5, 6, 7

and

4, 5, 5, 6, 30

the mode is 5.

The extreme score occurs only once, so it does not change the most frequent value.

An extreme score could affect the mode if that extreme value appeared frequently enough to become the most common score, but one isolated extreme value usually has no effect.

Summary of the effect of extreme scores

Measure	Effect of an isolated extreme score
Mean	Usually affected substantially because every value enters the calculation
Median	Usually affected little because it depends on the middle position
Mode	Usually unaffected because it depends on frequency

Should researchers remove extreme scores?

An extreme score should not automatically be deleted.

Researchers should consider:

• Whether it resulted from a recording error.

• Whether equipment failed.

• Whether the participant misunderstood instructions.

• Whether the value is a genuine part of the data.

• Whether rules for dealing with extreme values were established before analysis.

• Whether excluding it changes the conclusion.

If a genuine score is removed simply because it weakens the expected result, the analysis becomes biased.

A researcher may report results both with and without an unusual value, provided the decision is explained transparently.

Central tendency and distributions

Symmetrical distributions

In a perfectly symmetrical distribution with one clear peak:

• Mean

• Median

• Mode

may have the same value.

This is because the scores are balanced evenly around the centre.

Positively skewed distributions

A positively skewed distribution has a long tail extending towards higher scores.

The high scores in the tail pull the mean upwards.

The general pattern is:

Mode<Median<Mean

The exact relationship depends on the data, so apply this pattern only where the distribution is genuinely positively skewed.

Negatively skewed distributions

A negatively skewed distribution has a long tail extending towards lower scores.

The low scores in the tail pull the mean downwards.

The general pattern is:

Mean<Median<Mode

Again, the exact relationship depends on the particular data set.

Why the median is useful with skew

Because the median depends on position, it remains closer to the centre of most scores when a tail contains extreme values.

This is why researchers may choose the median when describing:

• Strongly skewed completion times.

• Ratings concentrated near one end of a scale.

• Data containing a small number of unusually high or low values.

Comparing experimental conditions

A psychologist may calculate one measure of central tendency for each condition.

Consider an experiment investigating noise and memory:

Condition	Mean recall score
Silence	15.8
Noise	12.2

The silent condition has the higher mean score.

The difference between the means is:

15.8−12.2=3.6

This describes the pattern in the sample.

It does not yet show:

• How spread out the scores were.

• Whether the groups overlapped.

• Whether the difference is statistically significant.

• Whether noise caused the difference.

• Whether the finding generalises to a wider population.

Researchers should consider measures of dispersion and, where appropriate, inferential testing.

The same mean can hide different distributions

Consider two conditions:

• Condition A: 4, 5, 5, 5, 6

• Condition B: 1, 2, 5, 8, 9

Both have a mean of 5.

However, scores in condition A are closely clustered around 5, while scores in condition B are much more dispersed.

The mean alone cannot show this difference. The researcher also needs a measure such as the range or standard deviation.

The same median can hide different scores

Consider:

• Data set A: 4, 5, 6, 7, 8

• Data set B: 1, 2, 6, 20, 40

Both have a median of 6.

The median accurately identifies the central position, but it does not show the substantial difference in spread.

The same mode can hide different distributions

Consider:

• Data set A: 4, 4, 4, 5, 6

• Data set B: 1, 2, 4, 4, 20

Both have a mode of 4.

The remaining scores are very different.

No measure of central tendency provides a complete description on its own.

Worked example: selecting an appropriate measure

A researcher asks 40 students which revision resource they use most often.

The response options are:

• Revision website

• Textbook

• Flashcards

• Practice paper

These are nominal categories.

The mode is the appropriate measure because it identifies the most frequently selected resource.

The mean cannot be calculated meaningfully because the categories do not have numerical values.

The median cannot be identified because the options do not have a necessary rank order.

Worked example: selecting the median

A psychologist records task-completion times:

18, 19, 20, 20, 21, 22, 80

The score of 80 is much higher than the others.

The mean is:

=(18+19+20+20+21+22+80)÷7

=200÷7

=28.57

The median is 20.

The median is likely to represent the typical completion time more effectively because the mean has been pulled upwards by the extreme score.

Worked example: selecting the mean

A psychologist records the number of targets identified correctly:

14, 15, 15, 16, 16, 17, 17

There are no obvious extreme scores, the values are numerical and the differences between scores are meaningful.

The mean is:

110÷7=15.71

The mean is appropriate because it uses all the information and is not being distorted by an extreme value.

Worked example: interpreting all three measures

A set of questionnaire scores is:

2, 3, 3, 4, 5, 7

Mean

=(2+3+3+4+5+7)÷6

=24÷6

=4

Median

The middle scores are 3 and 4:

(3+4)÷2=3.5

Mode

The most frequent score is 3.

Therefore:

• Mean = 4

• Median = 3.5

• Mode = 3

The measures differ because each defines the centre differently.

Measures of central tendency in psychological methods

Experiments

Researchers may calculate the mean or median dependent-variable score for each condition.

For example:

• Mean recall score.

• Median response time.

• Mean number of errors.

The choice depends on the level and distribution of the data.

Questionnaires

Researchers may use:

• Mean ratings where the measurement allows it.

• Median ordered responses.

• Modal response categories.

The wording and scoring of the questionnaire should be explained clearly.

Observations

Researchers may calculate:

• Mean frequency of behaviour.

• Median number of occurrences.

• Modal behavioural category.

The measure selected depends on how behaviour was recorded.

Correlations

Researchers may report the central tendency of each co-variable to describe the sample before examining the relationship between them.

For example:

• Mean hours of sleep.

• Median concentration score.

The correlation itself is then analysed separately.

Content analysis

Researchers may identify:

• The modal content category.

• Mean frequency of a coded behaviour per article.

• Median number of references within each item.

The coding categories must be operationalised consistently.

Presenting measures of central tendency

Measures of central tendency may appear in:

• Results sections.

• Summary tables.

• Graphs.

• Written comparisons.

• Statistical reports.

For example:

Condition	Mean score	Median score
Standard instructions	16.4	16
Encouraging instructions	18.7	19

The table should:

• Have a clear title.

• Label conditions accurately.

• State units where necessary.

• Use consistent decimal places.

• Report the selected statistic correctly.

You will develop these skills further when studying the construction and interpretation of data displays.

Measures of central tendency and research reports

In a scientific report:

• The method explains how scores were collected.

• The results present the measure of central tendency.

• The discussion interprets what the difference may mean.

For example:

Method

Performance was measured using the number of targets correctly identified in five minutes.

Results

The mean score was 18.2 in the silent condition and 14.7 in the noise condition.

Discussion

Participants in the silent condition obtained a higher mean score. This supports the prediction that performance would be better in silence, although other variables must be considered.

This preserves the distinction between presenting and interpreting evidence, as covered in reporting the stages of a psychological investigation.

Selecting a measure: decision process

Use the following process in an examination:

Step 1: Identify the level of measurement

Ask whether the data are:

• Nominal.

• Ordinal.

• Interval.

Step 2: Examine the distribution

Ask whether:

• Scores are reasonably balanced.

• The data are skewed.

• Extreme scores are present.

Step 3: Identify the purpose

Ask whether the researcher wants:

• An average using every score.

• The middle ordered score.

• The most frequent response.

Step 4: Select the measure

• Mode for nominal data or the most frequent response.

• Median for ordinal data, skewed data or data with extreme scores.

• Mean for suitable interval data without influential extreme scores.

Step 5: Justify the choice

Refer directly to the data.

Weak answer:

The median is better.

Stronger answer:

The median is more appropriate because the completion-time data contain an extreme score of 82 seconds. This would pull the mean upwards, whereas the median is based on the central position and is less affected.

Measures of central tendency A-Level Psychology revision: command words

Calculate

Show the stages of the calculation and give the final answer.

Identify

Name the correct measure.

Explain

Give a reason why the selected measure is appropriate.

Justify

Refer to the level of measurement, extreme scores or distribution.

Compare

State a similarity or difference between measures and explain its significance.

Interpret

Explain what the value tells us about the participants or conditions.

Checking your calculations

Before finalising an answer, check:

• Have all scores been included?

• Have the scores been placed in order for the median?

• Have you divided by the correct number of scores?

• Have frequencies been included correctly?

• Have you identified the most frequent value rather than the largest value?

• Have you handled an even number of scores correctly?

• Have you included the unit?

• Is the answer plausible given the original scores?

Quick plausibility checks

The mean should normally lie between the lowest and highest scores.

For example, if all scores lie between 10 and 20, a mean of 46 cannot be correct.

The median should come from the middle of the ordered distribution.

The mode should be the value with the greatest frequency, not the highest numerical score.

Key Words 🔑

Key word	Student-friendly definition	How it may be used in an exam
Descriptive statistics	Numerical techniques used to organise, summarise and present data.	Explain how psychologists describe the findings of an investigation.
Central tendency	The typical or central value within a data set.	Identify the purpose shared by the mean, median and mode.
Mean	The total of all scores divided by the number of scores.	Calculate an average or compare conditions.
Median	The middle value after scores have been placed in order.	Select a measure for ordered, skewed data or data containing extreme scores.
Mode	The most frequently occurring score or category.	Identify the most common response or summarise nominal data.
Frequency	The number of times a score or category occurs.	Identify the mode or calculate a mean from a frequency table.
Extreme score	A value much higher or lower than most other scores.	Explain why the mean may be distorted.
Nominal data	Data organised into categories without a meaningful order.	Justify selecting the mode.
Ordinal data	Data placed in rank order without assumed equal intervals.	Justify selecting the median or mode.
Interval data	Numerical data measured using meaningful equal units.	Justify calculating the mean where the distribution is suitable.
Skewed distribution	A distribution with scores extending into a longer tail on one side.	Explain why the mean and median may differ.
Modal category	The category occurring most frequently.	Report the central tendency of nominal data.
Bimodal	A data set with two values sharing the highest frequency.	Explain why a data set may have more than one mode.
Measure of dispersion	A statistic showing how spread out scores are.	Explain why central tendency alone gives an incomplete description.
Representative value	A value that provides a useful summary of the typical score.	Evaluate whether a mean or median reflects most participants.

Common Mistakes ⚠️

Mistake: Dividing by the wrong number when calculating the mean.

Why this is incorrect:The total must be divided by the number of scores, not by the highest score or the number of different values.

How to improve:Count every score, including repeated values, before dividing.

Mistake: Ignoring frequencies when calculating a mean from a table.

Why this is incorrect:A score occurring four times contributes four times to the total.

How to improve:Multiply each score by its frequency, add the products and divide by the total frequency.

Mistake: Finding the median before ordering the scores.

Why this is incorrect:The middle position is meaningful only after values are arranged from lowest to highest or highest to lowest.

How to improve:Always write the ordered data before identifying the middle.

Mistake: Selecting only one of the middle scores when there is an even number of values.

Why this is incorrect:An even data set has two central scores.

How to improve:Add the two middle values and divide by two.

Mistake: Identifying the highest score as the mode.

Why this is incorrect:The mode is the score occurring most frequently, not the score with the greatest numerical value.

How to improve:Count how often each value occurs.

Mistake: Claiming that every data set has a mode.

Why this is incorrect:A mode exists only when one or more values occur more frequently than the others.

How to improve:State “no mode” when every value has the same frequency.

Mistake: Reporting only one mode when two values share the highest frequency.

Why this is incorrect:Both values are modes.

How to improve:Describe the data set as bimodal and report both values.

Mistake: Calculating a mean for nominal categories.

Why this is incorrect:Unordered categories do not have meaningful numerical values that can be added and divided.

How to improve:Use the mode to identify the most frequent category.

Mistake: Assuming that the mean is always the best measure.

Why this is incorrect:Extreme scores or skew may make the mean unrepresentative.

How to improve:Check the level of measurement and distribution before selecting a measure.

Mistake: Saying that extreme scores never affect the median.

Why this is incorrect:The median is less affected, but changes that alter the order or central positions can change it.

How to improve:State that the median is usually less affected than the mean.

Mistake: Removing an extreme score without justification.

Why this is incorrect:The value may be genuine, and removing it may bias the findings.

How to improve:Investigate the reason for the score and report any exclusion procedure transparently.

Mistake: Comparing means without considering dispersion.

Why this is incorrect:Two groups may have the same mean but very different variation.

How to improve:Interpret central tendency alongside a range or standard deviation where available.

Exam-Style Questions ✍️

Question 1

Define the mean. (1 mark)

Question 2

Define the median. (1 mark)

Question 3

Define the mode. (1 mark)

Question 4

A psychologist records the following memory scores:

7, 4, 8, 6, 5

Calculate the mean, median and mode. (4 marks)

Question 5

Participants obtain the following concentration scores:

3, 5, 5, 6, 7, 8

Calculate the mean, median and mode. (4 marks)

Question 6

A researcher records the following scores:

Score	Frequency
1	2
2	3
3	4
4	1

Calculate the mean, median and mode. Show your working. (6 marks)

Question 7

A psychologist records the following completion times:

21, 22, 22, 23, 24, 25, 89

Identify the most appropriate measure of central tendency and justify your answer. (3 marks)

Question 8

A questionnaire asks participants to select their preferred revision resource from four unordered categories.

Explain which measure of central tendency should be used. (2 marks)

Question 9

Explain how one extremely high score may affect:

1. The mean

2. The median

3. The mode

(6 marks)

Question 10

The scores from two conditions are shown below.

Condition A	Condition B
4	1
5	2
5	5
5	8
6	9

Calculate the mean and median for each condition. Explain why measures of central tendency alone do not provide a complete comparison. (8 marks)

Question 11

A researcher obtains ordinal ratings of satisfaction from 50 participants. A small number of ratings are extremely low.

Explain why the median may be more appropriate than the mean. (4 marks)

Question 12

Discuss the usefulness of the mean, median and mode as measures of central tendency. Refer to:

• Levels of measurement

• Use of all scores

• Extreme scores

• Skewed distributions

• Data interpretation

(8 marks)