Stuck on the Maths in A-Level Psychology? Research Methods Calculations Made Clear
You understand the experiment. You can identify the independent variable and explain why the researcher used repeated measures.
Then the question asks you to calculate a percentage or interpret an average—and suddenly you feel less confident.
If the maths in A-Level Psychology is where you get stuck, start by separating two tasks: performing a calculation and explaining what the result means.
This guide walks you through common calculations using Psychology examples. It also explains how to use an AI maths tool to check your understanding without letting it do all the thinking.
The revised AQA A-Level Psychology specification includes calculating the mean, median, mode, range and percentages, alongside interpreting data and understanding statistical testing. AQA
Start with the question, not the calculator
Before entering numbers, identify what you are being asked to find.
| Question asks for… | Your starting point |
|---|---|
| Mean | Add the scores, then divide by the number of scores |
| Median | Put the scores in order and find the middle |
| Mode | Find the most frequent score |
| Range | Subtract the lowest score from the highest |
| Percentage | Identify the part and the relevant total |
| Interpretation | Explain the result in the context of the investigation |
A correct calculation can still lead to an incorrect answer if you use the wrong denominator or explain a different measure.
Mean, median and mode: three different summaries
Imagine five participants recall the following numbers of words:
4, 5, 5, 6, 10
These are fictional practice data.
Calculate the mean
Add the scores:
4 + 5 + 5 + 6 + 10 = 30
Divide by the number of participants:
30 ÷ 5 = 6
The mean is six words recalled.
A common mistake is dividing by the highest score rather than the number of scores. Here, there are five participants, so the denominator is five.
Find the median
The scores are already in ascending order:
4, 5, 5, 6, 10
The middle score is 5, so the median is five words recalled.
With an even number of scores, calculate the mean of the two middle values.
For example:
3, 4, 6, 9
The median is:
(4 + 6) ÷ 2 = 5
The median does not have to be a score that an individual participant obtained.
Find the mode
The most frequent score is 5, appearing twice.
The mode is therefore five words recalled.
A dataset may have more than one mode, or no single most frequent value.
Why are the mean and median different?
In our first dataset, the score of 10 pulls the mean upwards.
The median depends on the middle position, so the high score has less influence on it.
Application question: Why might the median be useful when one participant has an unusually high recall score?
Model answer: The median is less affected by the unusually high score, so it may provide a more useful description of typical recall performance in this dataset.
Range: how spread out are the scores?
Using the original scores:
4, 5, 5, 6, 10
Calculate:
Highest − lowest = 10 − 4 = 6
The range is six words.
Do not add one to the answer. You are calculating the difference between the endpoints.
The range describes spread, but it only uses the highest and lowest scores. It does not tell you how the remaining scores are distributed.
Consider:
- Dataset A: 4, 5, 5, 6, 10
- Dataset B: 4, 4, 9, 10, 10
Both have a range of six, despite different patterns within the datasets.
Standard deviation: what does it tell you?
Standard deviation is another measure of dispersion. It describes how spread out scores are around the mean, taking all the scores into account.
For comparable measures:
- A smaller standard deviation indicates scores clustered more closely around the mean.
- A larger standard deviation indicates greater spread.
Suppose two fictional groups both have a mean recall score of eight words:
| Group | Mean | Standard deviation |
|---|---|---|
| A | 8 | 1 |
| B | 8 | 3 |
Group B’s scores are more dispersed around the mean.
This does not automatically mean Group B’s study is less reliable. Variation between participants is different from consistency of measurement.
Percentages: check the denominator
Suppose 18 of 24 participants correctly identify an image.
Use:
Percentage = (part ÷ total) × 100
Therefore:
(18 ÷ 24) × 100 = 75%
The important decision is identifying the relevant total.
If the question asks for the percentage of participants in one condition, use the number in that condition—not automatically the entire sample.
Try it yourself
Question: Seven of 20 participants select the correct answer. What percentage is this?
Answer: (7 ÷ 20) × 100 = 35%
Include the percentage symbol and show your working when requested.
Use AI to explain the step where you got stuck
An AI tool can provide an additional explanation when your notes or worked example leave you confused.
The AI Math Problem Solver is a Chrome extension whose listing describes step-by-step mathematical solutions. You could use a tool of this kind to compare its working with your own calculation. Check its current access terms, permissions and any charges before installing or using it. Chrome Web Store
Use this sequence:
- Attempt the calculation yourself.
- Write down where you became unsure.
- Request an explanation of that specific step.
- Check it against your textbook, teacher’s example or another trusted resource.
- Complete a similar question without assistance.
For example:
“I added these five scores correctly but used the wrong denominator. Explain how to identify the denominator when calculating a mean. Then give me a similar question without revealing the answer.”
The useful outcome is being able to repeat the process independently.
AI cannot choose a statistical test from numbers alone
Choosing an inferential test requires information about the investigation.
You need to consider:
- Whether it investigates a difference or a correlation.
- Whether the design produces related or unrelated data.
- The level of measurement.
A spreadsheet of scores may not reveal all of this.
Before asking for help, identify how participants were allocated. Our comparison of independent groups and repeated measures designs can help you distinguish unrelated and related observations.
Do not accept a suggested test simply because the explanation sounds confident.
Calculations need clearly defined measurements
Numbers become meaningful when you know what they represent.
A score of “8” could mean eight words recalled, a rating on a questionnaire or eight observed behaviours.
That is why operationalisation in Psychology matters: it defines how a variable is measured.
Before interpreting a table, check its headings, units and scoring system.
Turn the result into a Psychology answer
Compare these responses:
Vague: “Group A did better.”
Applied: “Group A recalled a mean of eight words, compared with six in Group B, indicating higher average recall in this sample.”
The applied answer identifies the measure, outcome and relevant comparison.
It does not claim that the difference is statistically significant without an appropriate analysis.
For further support, our guide to AO2 application in A-Level Psychology explains how to connect knowledge to the details of a question.
A short practice task
Six participants recall:
2, 4, 4, 6, 7, 7
Find the mean, median, mode and range before checking below.
Worked answers
Mean:
Total = 30.
30 ÷ 6 = 5 words.
Median:
The middle scores are 4 and 6.
(4 + 6) ÷ 2 = 5 words.
Mode:
4 and 7 words. Both appear twice.
Range:
7 − 2 = 5 words.
If you made a mistake, identify the step rather than simply copying the answer. Did you forget to order the scores, overlook a second mode or use the wrong denominator?
Our AQA Research Methods resource collection provides further materials for developing these skills.
Your goal is to leave each practice session able to explain what you calculated, how you calculated it and what it means in the study.