Revision notes for AQA GCSE Psychology Arithmetic and numerical computation. Open the guide for explanations and worked examples. Written against the AQA GCSE Psychology (8182) specification, so the content matches what's examinable rather than general Psychology background.
Arithmetic and numerical computation
What you'll learn
- How to recognise and use decimals and standard form in psychology data.
- How to work with ratios, fractions and percentages.
- How to estimate answers so you can spot mistakes quickly.
- How these maths skills appear in GCSE Psychology research contexts.
Why maths appears in Psychology
Psychology is the scientific study of the mind and behaviour. That means psychologists often collect numerical data, such as memory scores, questionnaire ratings, reaction times, or the number of participants who gave a particular response.
You do not need advanced statistics for GCSE Psychology. You do need to be confident with the basic number skills that help you describe and interpret research findings.
Key Idea
The big idea
Arithmetic helps you turn raw results into meaningful statements, such as “60% of participants conformed” or “the ratio of boys to girls was 3:2”.
Decimals
A decimal is a number written using a decimal point, such as 0.5, 2.75 or 10.4. Decimals are useful in psychology when results are averages, proportions, questionnaire scores, or rounded values.
Definition
Decimal
A decimal is a number written with a decimal point to show parts of a whole number.
Place value
The position of a digit tells you its value.
For example, in 3.47:
- 3 is the number of ones.
- 4 is the number of tenths.
- 7 is the number of hundredths.
So 3.47 means 3 whole ones, 4 tenths and 7 hundredths.
Decimals in psychology
You might see decimals when reading results like:
- “The mean recall score was 6.8 words.”
- “The average rating for anxiety was 4.5 out of 10.”
- “0.25 of the sample gave the same answer.”
Decimals are especially useful when the answer is not a whole number.
Example
Interpreting a decimal proportion
A study found that 0.75 of participants agreed with a group judgement.
- Treat 0.75 as a proportion of the whole sample, where 1.00 would mean all participants.
- Convert the decimal to a percentage by multiplying by 100: 0.75 becomes 75%.
- Interpret the result: 75% of participants agreed with the group judgement.
Common Mistake
Forgetting that 0.5 means half
0.5 is not “a small amount close to nothing”. It means one half, or 50%. Similarly, 0.25 means one quarter, or 25%.
Standard form
Very large or very small numbers can be awkward to write. Standard form is a shorter way to write them.
Definition
Standard form
Standard form writes a number as a×10na \times 10^na×10n, where aaa is at least 1 but less than 10, and nnn is a whole number showing how many places the decimal point moves.
For example:
- 3.2×1043.2 \times 10^43.2×104 means 32,000.
- 5.6×10−35.6 \times 10^{-3}5.6×10−3 means 0.0056.
At GCSE Psychology, you only need to recognise and use standard form when it appears in data. You are not expected to use advanced statistical tests.
Positive powers of 10
A positive power means the ordinary number is large.
For example, 4.5×1034.5 \times 10^34.5×103 means move the decimal point 3 places to the right:
4.5 becomes 4500.
Negative powers of 10
A negative power means the ordinary number is small.
For example, 2.1×10−22.1 \times 10^{-2}2.1×10−2 means move the decimal point 2 places to the left:
2.1 becomes 0.021.
Example
Converting standard form into an ordinary number
A research summary writes the number of responses as 6.4×1026.4 \times 10^26.4×102.
- Notice that the power is positive: 10210^2102 means the number will get larger.
- Move the decimal point 2 places to the right: 6.4 becomes 640.
- Interpret the value: 6.4×1026.4 \times 10^26.4×102 means 640 responses.
Tip
Standard form direction check
Positive power: move right and make the number bigger. Negative power: move left and make the number smaller.
Fractions
A fraction shows part of a whole. It has a numerator, which is the top number, and a denominator, which is the bottom number.
Definition
Fraction
A fraction shows how many equal parts of a whole are being considered, such as 35\frac{3}{5}53, meaning 3 parts out of 5.
In psychology, fractions often describe how many participants showed a behaviour or gave a response.
For example:
- 1220\frac{12}{20}2012 participants recalled the first word in a list.
- 510\frac{5}{10}105 participants chose the same line as the majority in a conformity task.
Fractions are often converted into percentages because percentages are easier to compare.
Percentages
A percentage means “out of 100”. The symbol is %. Percentages are very common in research reports because they make samples of different sizes easier to compare.
Definition
Percentage
A percentage is a proportion written as a number out of 100.
For example:
- 50% means 50 out of 100, or one half.
- 25% means 25 out of 100, or one quarter.
- 10% means 10 out of 100, or one tenth.
Converting a fraction to a percentage
To convert a fraction to a percentage:
- Divide the numerator by the denominator.
- Multiply by 100.
Example
Turning participant responses into a percentage
In a small practical activity, 18 out of 30 participants remembered the first item in a word list. What percentage is this?
- Write the result as a fraction: 1830\frac{18}{30}3018.
- Divide 18 by 30 to turn the fraction into a decimal: 18 divided by 30 gives 0.6.
- Multiply the decimal by 100 to convert it into a percentage: 0.6 becomes 60%.
- Interpret the result in context: 60% of participants remembered the first item.
Converting a percentage to a number of participants
Sometimes you are given the percentage and need to work out how many people it represents.
Example
Finding the number of participants from a percentage
A class study has 40 participants. 25% report feeling more confident after a short intervention. How many participants is this?
- Convert 25% into a decimal by dividing by 100: 25% becomes 0.25.
- Multiply the decimal by the total number of participants: 0.25 of 40 is 10.
- Interpret the result: 10 participants reported feeling more confident.
Common Mistake
Mixing up percentage and number of people
40% is not the same as 40 people unless the total sample size is 100. Always check the total number of participants.
Ratios
A ratio compares amounts. It tells you how much of one thing there is compared with another.
Definition
Ratio
A ratio compares two or more quantities, such as 3:2, meaning 3 parts of one quantity for every 2 parts of another.
In psychology, ratios might describe a sample. For example:
- The ratio of boys to girls was 3:2.
- The ratio of participants in condition A to condition B was 1:1.
- The ratio of correct to incorrect responses was 4:1.
Simplifying ratios
A ratio should usually be simplified by dividing both sides by the same number.
For example, 12:8 simplifies to 3:2 because both numbers can be divided by 4.
Example
Simplifying a sample ratio
A study has 18 participants in condition A and 12 participants in condition B. Write the ratio of condition A to condition B in its simplest form.
- Start with the ratio 18:12 because there are 18 in condition A and 12 in condition B.
- Find a number that divides both sides exactly: both 18 and 12 can be divided by 6.
- Divide both parts by 6: 18 becomes 3, and 12 becomes 2.
- State the simplified ratio: the ratio of condition A to condition B is 3:2.
Working with ratios and totals
If a ratio is 3:2, there are 5 parts altogether. That does not mean there are only 5 people. It means the total group is split into 5 equal parts.
Example
Using a ratio to split participants
A sample of 50 participants has a ratio of 3:2 for left-handed to right-handed participants. How many are left-handed?
- Add the parts of the ratio: 3 parts plus 2 parts gives 5 parts in total.
- Divide the total number of participants by the total parts: 50 divided into 5 equal parts gives 10 participants per part.
- Multiply by the left-handed part of the ratio: 3 parts of 10 gives 30.
- Interpret the result: 30 participants are left-handed.
Estimation
Estimation means finding an approximate answer. You use estimation to check whether a calculated answer is sensible.
Definition
Estimation
Estimation is working out a rough answer, usually by rounding numbers, to check whether an exact answer is reasonable.
In GCSE Psychology, estimation is useful when checking:
- percentages,
- averages,
- totals in frequency tables,
- values read from graphs,
- whether a calculator answer makes sense.
Rounding before calculating
To estimate, round numbers to easier values.
For example:
- 49 can be rounded to 50.
- 19.8 can be rounded to 20.
- 101 can be rounded to 100.
You do not use the estimated answer as your final answer if the question asks for an exact calculation. You use it as a check.
Example
Estimating a percentage calculation
A questionnaire was completed by 198 students. About 51% said they used revision flashcards. Estimate how many students this is.
- Round 198 to 200 because it is very close to 200.
- Round 51% to 50% because it is very close to half.
- Find half of 200, which is 100.
- Use the estimate to check the likely answer: the exact answer should be close to 100 students.
Tip
Use estimation as a warning system
If your exact calculation gives 10 students or 1000 students in the example above, estimation tells you something has gone wrong.
Bringing the skills together
Psychology questions often combine number skills. You may need to read a scenario, choose the right calculation, then interpret the result in words.
For example, a question might describe a class experiment on memory and ask what percentage of participants recalled a word correctly. You would identify the number who recalled it, compare it with the total sample, convert to a percentage, and link it back to the psychological finding.
Example
Combining fractions, percentages and interpretation
In a memory practical, 24 out of 40 participants correctly recall a word shown at the start of a list. What percentage recalled it, and what might this suggest?
- Express the result as a fraction of the total sample: 2440\frac{24}{40}4024.
- Divide 24 by 40 to convert the fraction into a decimal: 24 divided by 40 gives 0.6.
- Convert 0.6 into a percentage by multiplying by 100: 0.6 becomes 60%.
- Interpret the finding: 60% recalled the first word, which could suggest stronger recall for early items in a word list.
Common Mistake
Do not add extra statistics
For GCSE Psychology, you describe patterns from data, graphs and simple calculations. You do not need to calculate p-values, standard deviation, chi-square, Mann-Whitney, sign test, or a correlation coefficient.
How this links to AO skills
AO1: Knowledge and understanding
You need to know what decimals, standard form, ratios, fractions, percentages and estimation are.
AO2: Application
You need to apply these skills to psychology scenarios, such as participant responses, memory scores, questionnaire ratings, or results from an investigation.
AO3: Analysis and evaluation
You may need to judge whether a numerical conclusion is sensible. For example, if a sample has only 20 participants, claiming “95% proves the result is true for everyone” would be too strong. Percentages describe the sample, but they do not automatically prove something about all people.
Exam technique
In the exam
- Identify what the question is asking for: decimal, standard form, ratio, fraction, percentage, or estimate.
- Keep the psychology context in your final interpretation, such as “participants”, “responses”, “recall” or “questionnaire score”.
- Use estimation to check that your answer is sensible before moving on.
Self review
Check yourself
- If 15 out of 60 participants gave the same answer, how would you convert this into a percentage?
- What does the ratio 2:3 tell you about two groups in a sample?
- How could estimation help you spot an impossible answer in a psychology data question?