Tables and graphs | AQA A-Level Psychology Revision
- Revision Notes
- Aug 4
- 15 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
This Tables and graphs A-Level Psychology revision page explains how psychologists organise, present and interpret quantitative data. You will learn how to construct clear tables, bar charts and histograms, as well as how to select an appropriate display for a particular data set. These skills form part of AQA Research Methods and may be assessed through unfamiliar results or practical research scenarios. Accurate displays depend on calculations covered in percentages, ratios and numerical data, so always check your values before plotting them.
Learning Objectives 🎯
By the end of this revision page, you should be able to:
Construct clear tables containing psychological data.
Interpret frequencies, patterns and differences presented in tables.
Construct correctly labelled bar charts.
Construct correctly labelled histograms.
Compare the features and uses of bar charts and histograms.
Select an appropriate display for a given psychological data set.
Revision Notes 📚
Why tables and graphs matter in A-Level Psychology
Psychologists collect data through experiments, observations, questionnaires, interviews and other research methods. Raw numerical data can be difficult to understand, particularly when a study includes many participants or observations.
Tables and graphs organise these results so that patterns can be identified more easily.
AQA requires students to be able to construct and interpret:
frequency tables and diagrams;
bar charts;
histograms.
Students must also be able to translate information between numerical and graphical forms. For example, you could be given a record sheet containing numerical scores and asked to construct an appropriate graph.
Tables and graphs may help researchers:
summarise large data sets;
compare conditions or groups;
identify the most and least frequent results;
recognise patterns in scores;
communicate findings clearly;
support the analysis and interpretation of quantitative data.
The numerical summaries included in a table or graph may come from calculations covered in measures of central tendency and measures of dispersion.
Quantitative data
Quantitative data consist of numerical values.
Examples might include:
the number of words recalled;
a score on a questionnaire;
the frequency of an observed behaviour;
the time taken to complete a task;
the number of participants giving each response.
Tables, bar charts and histograms are used to organise and display quantitative data.
The appropriate display depends on:
what the numbers represent;
whether the values are separate categories or grouped numerical intervals;
whether exact figures or an overall pattern need to be communicated.
Constructing a table
A table organises data into rows and columns.
A well-constructed table allows the reader to identify:
what was measured;
the values or categories included;
the frequency or score associated with each value;
any totals or calculated statistics;
the units used.
Features of a clear table
A suitable table should normally include:
A clear and informative title.
Clearly labelled columns and rows.
Appropriate units where measurements are used.
Values arranged in a logical order.
A consistent number of decimal places or significant figures.
A total row where this is useful.
No unnecessary information.
A title such as Results is usually too vague. A more informative title would be:
Number of participants recalling each number of words
Frequency tables
A frequency table shows how often each score, response or behaviour occurs.
The word frequency means the number of times something occurs.
Consider the following raw scores for the number of words recalled by \(15\) participants:
$$4,\ 6,\ 5,\ 7,\ 6,\ 5,\ 4,\ 8,\ 6,\ 7,\ 5,\ 6,\ 4,\ 5,\ 6$$
To construct a frequency table:
Identify each different score.
Arrange the scores in numerical order.
Count how often each score occurs.
Record each frequency.
Check that the frequencies total the number of scores in the original data set.
The completed table would be:
Number of words recalled | Frequency |
\(4\) | \(3\) |
\(5\) | \(4\) |
\(6\) | \(5\) |
\(7\) | \(2\) |
\(8\) | \(1\) |
Total | \(15\) |
The total frequency can be checked using:
$$3+4+5+2+1=15$$
The total matches the number of participants, so no score appears to have been missed.
Interpreting a frequency table
When interpreting a table, read the title and column headings before looking at individual values.
From the previous table, you can identify that:
the most frequent score was \(6\) words;
\(5\) participants recalled \(6\) words;
the least frequent score was \(8\) words;
the scores ranged from \(4\) to \(8\) words;
there were \(15\) participants in total.
You could also calculate the proportion of participants achieving a particular score.
For example, the percentage recalling \(6\) words is:
$$\frac{5}{15}\times100=33.333\ldots\%$$
To three significant figures:
$$\boxed{33.3\%}$$
Tables comparing conditions
Tables are often used to compare results from two or more conditions.
For example:
Measure | Quiet condition | Noise condition |
Mean number of words recalled | \(12.4\) | \(8.7\) |
Median number of words recalled | \(12.0\) | \(9.0\) |
Range | \(6\) | \(11\) |
This table allows the reader to compare both the typical scores and the spread of scores.
The table suggests that:
recall was higher in the quiet condition;
the scores were more widely spread in the noise condition;
the mean and median were similar within each condition.
A table presents exact values clearly, but a graph may make the overall difference between the conditions easier to see.
Interpreting tables accurately
When answering a question based on a table:
Read the title.
Identify what each row and column represents.
Check the units.
Examine the scale or numerical precision.
Compare the correct values.
Use figures from the table to support your interpretation.
For example, rather than writing:
Participants performed better in the quiet condition.
A more precise interpretation would be:
The mean recall score was higher in the quiet condition, at \(12.4\) words, than in the noise condition, at \(8.7\) words.
Using relevant figures demonstrates that your interpretation is based on the data.
Bar charts
A bar chart displays values using separate rectangular bars.
The height of each bar represents a frequency, score, percentage or other numerical value.
Bar charts are useful when the horizontal axis contains separate groups, conditions or categories.
Examples include:
different experimental conditions;
types of observed behaviour;
questionnaire response categories;
attachment classifications;
categories of participant.
Features of a bar chart
A correctly constructed bar chart should include:
a clear title;
a labelled horizontal axis;
a labelled vertical axis;
units where appropriate;
a suitable and evenly spaced scale;
bars of equal width;
gaps between the bars;
accurately plotted values.
The gaps are important because each bar represents a separate category or condition.
Worked example: planning a bar chart
A researcher records the following questionnaire responses:
Response | Frequency |
Agree | \(18\) |
Neither agree nor disagree | \(9\) |
Disagree | \(13\) |
A suitable bar chart would use:
horizontal axis: response category;
vertical axis: frequency;
bar heights: \(18\), \(9\) and \(13\);
gaps: between all three bars;
title: Frequency of questionnaire responses.
The vertical scale must be large enough to include the highest value of \(18\).
A suitable scale might increase in intervals of \(2\):
$$0,\ 2,\ 4,\ 6,\ 8,\ 10,\ 12,\ 14,\ 16,\ 18,\ 20$$
Selecting a scale for a bar chart
A graph scale should:
include all the data;
increase in equal intervals;
use most of the available plotting area;
be straightforward to interpret;
avoid unnecessary complexity.
Suppose the highest frequency is \(42\). A scale increasing in intervals of \(5\) would be reasonable:
$$0,\ 5,\ 10,\ 15,\ 20,\ 25,\ 30,\ 35,\ 40,\ 45$$
A scale such as the following would not be suitable:
$$0,\ 5,\ 10,\ 20,\ 30,\ 42$$
This is because the intervals are inconsistent.
Constructing a bar chart
Use the following process:
Read the data and identify the categories.
Decide which variable belongs on each axis.
Draw and label the axes.
Select a suitable scale.
Mark equal intervals on the vertical axis.
Draw bars of equal width.
Leave equal gaps between the bars.
Plot each value accurately.
Add a clear title.
Check every bar against the original data.
Worked example: comparing experimental conditions
A researcher investigates the number of words recalled under three conditions.
Condition | Mean number of words recalled |
No background sound | \(15.2\) |
Quiet instrumental music | \(12.8\) |
Speech recording | \(9.4\) |
A bar chart would be appropriate because the three conditions are separate categories.
The chart should contain:
the three conditions on the horizontal axis;
mean number of words recalled on the vertical axis;
separate bars with heights of \(15.2\), \(12.8\) and \(9.4\);
gaps between the bars.
The chart would show that the highest mean recall occurred in the no-background-sound condition.
Interpreting a bar chart
When interpreting a bar chart:
read the title;
check both axis labels;
examine the scale;
identify the tallest and shortest bars;
compare relevant categories;
use numerical values where possible;
avoid describing a difference as significant unless statistical significance has been established.
For example:
Mean recall was highest in the no-background-sound condition at \(15.2\) words and lowest in the speech-recording condition at \(9.4\) words.
The difference between these means is:
$$15.2-9.4=5.8$$
Therefore, the mean recall score was \(5.8\) words higher without background sound.
Bar chart or table?
A table and a bar chart can present the same data, but they emphasise different features.
Display | Main advantage |
Table | Shows exact numerical values clearly |
Bar chart | Makes comparisons between categories visually clear |
A table may be more appropriate when the reader needs precise values.
A bar chart may be more appropriate when the main aim is to show differences between groups or conditions.
Histograms
A histogram uses adjoining bars to display numerical data grouped into intervals.
Unlike a bar chart, the horizontal axis of a histogram represents a numerical scale rather than separate named categories.
For example, response times could be grouped into intervals such as:
\(0 \leq x < 5\) seconds;
\(5 \leq x < 10\) seconds;
\(10 \leq x < 15\) seconds;
\(15 \leq x < 20\) seconds.
The bars touch because the intervals form a continuous numerical sequence.
Features of a histogram
A correctly constructed histogram should include:
a clear title;
a labelled horizontal axis;
a labelled vertical axis;
units where appropriate;
grouped numerical intervals on the horizontal axis;
a consistent scale;
adjoining bars with no gaps;
accurately plotted frequencies.
Worked example: grouped scores
A psychologist records the time taken by participants to complete a task.
Completion time in seconds | Frequency |
\(0 \leq x < 5\) | \(2\) |
\(5 \leq x < 10\) | \(7\) |
\(10 \leq x < 15\) | \(11\) |
\(15 \leq x < 20\) | \(6\) |
\(20 \leq x < 25\) | \(4\) |
The total number of participants is:
$$2+7+11+6+4=30$$
A suitable histogram would have:
completion time in seconds on the horizontal axis;
frequency on the vertical axis;
five adjoining bars;
bar heights of \(2\), \(7\), \(11\), \(6\) and \(4\).
The interval with the highest frequency is:
$$10 \leq x < 15$$
This means that more participants completed the task within this interval than within any other listed interval.
Interpreting intervals
An interval written as:
$$10 \leq x < 15$$
includes values that are:
equal to or greater than \(10\);
less than \(15\).
A score of \(10\) would be placed in this interval.
A score of \(15\) would be placed in the next interval:
$$15 \leq x < 20$$
This prevents a value from being counted in two intervals.
Constructing a histogram
Use the following process:
Identify the numerical variable.
Check how the values have been grouped.
Draw and label both axes.
Write the numerical intervals in the correct order.
Select an even scale for the frequency axis.
Draw adjoining bars.
Plot each frequency accurately.
Add a clear title.
Check the graph against the original frequency table.
Interpreting a histogram
A histogram can help you identify:
the interval containing the most scores;
the interval containing the fewest scores;
the overall spread of the results;
whether scores are concentrated within a particular part of the scale;
the approximate shape of the distribution.
The detailed features of symmetrical and skewed data are covered in distributions.
When interpreting a histogram, remember that each bar represents an interval, not necessarily one exact score.
For example, a frequency of \(11\) for the interval:
$$10 \leq x < 15$$
means that \(11\) scores fall somewhere from \(10\) up to, but not including, \(15\).
It does not mean that \(11\) participants all achieved a score of \(10\).
Bar charts and histograms compared
Feature | Bar chart | Histogram |
Horizontal axis | Separate categories, groups or conditions | Adjoining numerical intervals |
Bars | Separated by gaps | Touch one another |
Order of bars | May depend on the categories | Follows the numerical scale |
Main purpose | Compare separate categories | Show the frequency of grouped numerical values |
Example | Frequency of different questionnaire responses | Frequency of scores within numerical intervals |
The most visible distinction is that bar-chart bars are separated, whereas histogram bars touch.
However, do not select a display based only on appearance. First identify the type and organisation of the data.
Choosing an appropriate display
A question may ask you to identify, select or justify an appropriate display.
Use the information below as a guide.
Data or purpose | Appropriate display |
Exact values need to be presented clearly | Table |
Frequencies of separate categories need to be compared | Bar chart |
Mean scores from separate conditions need to be compared | Bar chart |
Numerical scores are grouped into adjoining intervals | Histogram |
The frequency and pattern of grouped numerical values need to be shown | Histogram |
A relationship between two co-variables needs to be displayed | Scattergram |
Scattergrams and the interpretation of relationships are covered in scattergrams and correlation coefficients.
Your choice may also depend on whether the results use nominal, ordinal or interval data. These distinctions are developed in levels of measurement.
Selecting a display: worked scenarios
Scenario 1: questionnaire categories
A researcher records how many participants select:
strongly agree;
agree;
neither agree nor disagree;
disagree;
strongly disagree.
A bar chart would be suitable because each response is presented as a separate category.
Scenario 2: grouped response times
A researcher groups response times into the intervals:
$$0 \leq x < 1$$
$$1 \leq x < 2$$
$$2 \leq x < 3$$
$$3 \leq x < 4$$
A histogram would be suitable because the values have been arranged into adjoining numerical intervals.
Scenario 3: complete results
A teacher wants to show the exact mean and range for two experimental conditions.
A table would be suitable because it allows the exact values for both statistics to be read directly.
Scenario 4: two co-variables
A researcher records each participant’s amount of sleep and memory score.
A scattergram would be suitable because the researcher is examining a possible relationship between two co-variables.
Translating numerical information into a graph
AQA may provide numerical information in one form and ask you to present it in another form.
For example, you could be given this table:
Type of behaviour | Frequency |
Smiling | \(16\) |
Looking away | \(11\) |
Asking a question | \(8\) |
Interrupting | \(5\) |
You might then be asked to construct a bar chart.
To translate the data accurately:
Preserve the category labels.
Copy each frequency correctly.
Select a scale that includes the highest frequency.
Plot the bars at the correct heights.
Add labels and a title.
Check the graph against the table.
These skills are developed further in translating and presenting data.
Translating a graph into numerical information
You may also be asked to extract values from a graph and place them in a table.
To do this:
Identify the category or interval.
Trace the top of the bar across to the vertical scale.
read the value carefully;
record the number in the correct row;
check the units;
maintain consistent numerical precision.
Take particular care when the scale increases in intervals greater than \(1\).
For example, if the scale is:
$$0,\ 5,\ 10,\ 15,\ 20$$
each smaller division may represent a value other than \(1\). Work out the value of each division before reading the graph.
Presenting results without misleading the reader
A data display should represent the results accurately.
To avoid creating a misleading display:
use equal scale intervals;
label the axes clearly;
include units;
make bar widths consistent;
plot every value accurately;
do not omit relevant categories;
distinguish clearly between bar charts and histograms;
use the same numerical precision for comparable results.
A graph should make the results clearer, not distort them.
Key Words 🔑
Key word | Student-friendly definition | How it may be used in an exam |
Table | A display that organises data into labelled rows and columns. | You may be asked to construct a table or interpret values presented within one. |
Frequency | The number of times a score, response or behaviour occurs. | Frequencies may be entered into a table or represented by the heights of bars. |
Frequency table | A table showing how often each score, response or category occurs. | You may need to construct one from raw data. |
Bar chart | A graph using separate bars to compare categories, groups or conditions. | You may construct one from categorical frequencies or mean scores. |
Histogram | A graph using adjoining bars to show numerical data grouped into intervals. | You may construct or interpret one using grouped scores. |
Axis | A reference line on a graph showing the variable or measurement being displayed. | Both axes should be labelled correctly when constructing a graph. |
Scale | The ordered numerical values marked along an axis. | You must select and interpret suitable, equal scale intervals. |
Category | A named group into which data have been classified. | Separate categories may be displayed using a bar chart. |
Interval | A defined section of a numerical scale containing a range of values. | Grouped numerical intervals may be displayed using a histogram. |
Quantitative data | Data expressed numerically. | Tables and graphs are commonly used to present quantitative results. |
Title | A brief description explaining what a table or graph shows. | A suitable title is an important feature of a complete display. |
Unit | The measurement used for a numerical value, such as seconds. | Units should be included in a table heading or axis label where appropriate. |
Common Mistakes ⚠️
Mistake: Using an unclear title such as “Results”.
Why this is incorrect:
The reader cannot identify what the values represent without additional information.
How to improve:
Write a title that identifies both the measure and the relevant groups or conditions.
For example:
Mean number of words recalled in each experimental condition
Mistake: Leaving the axes unlabelled.
Why this is incorrect:
A graph is difficult or impossible to interpret if the reader does not know what each axis represents.
How to improve:
Label both axes before drawing any bars and include measurement units where appropriate.
Mistake: Using unequal intervals on the numerical scale.
Why this is incorrect:
Unequal intervals distort the visual size of differences and may misrepresent the data.
How to improve:
Check that the scale increases by the same amount at every step.
For example:
$$0,\ 5,\ 10,\ 15,\ 20$$
Mistake: Allowing the bars of a bar chart to touch.
Why this is incorrect:
The bars represent separate categories, groups or conditions.
How to improve:
Leave equal gaps between the bars of a bar chart.
Mistake: Leaving gaps between the bars of a histogram.
Why this is incorrect:
The bars represent adjoining intervals on a numerical scale.
How to improve:
Draw histogram bars so that they touch.
Mistake: Selecting a bar chart for grouped numerical intervals.
Why this is incorrect:
A bar chart treats each label as a separate category, whereas grouped numerical intervals form an ordered numerical scale.
How to improve:
Use a histogram when values are grouped into adjoining numerical intervals.
Mistake: Selecting a histogram for separate experimental conditions.
Why this is incorrect:
Conditions such as control, low-noise and high-noise are separate categories rather than numerical intervals.
How to improve:
Use a bar chart to compare separate conditions.
Mistake: Plotting bar heights inaccurately.
Why this is incorrect:
The graph will not represent the original results correctly.
How to improve:
Draw light guide lines from each value on the vertical axis and check every plotted bar against the data table.
Mistake: Failing to include units.
Why this is incorrect:
A numerical value such as \(12\) could represent seconds, words, points or another measurement.
How to improve:
Include the unit in the relevant table heading or axis label.
Mistake: Describing a difference as statistically significant from a graph alone.
Why this is incorrect:
A visual difference does not show whether the result meets an appropriate level of statistical significance.
How to improve:
Describe the observed pattern or difference without using the term significant unless the outcome of an inferential test is provided.
Mistake: Reading an interval as one exact score.
Why this is incorrect:
A histogram bar represents every score falling within the stated interval.
How to improve:
Refer to the interval as a range.
For example:
$$10 \leq x < 15$$
means values from \(10\) up to, but not including, \(15\).
Exam-Style Questions ✍️
Question 1
State one feature of a correctly constructed table.[1 mark]
Question 2
A researcher records the following memory scores:
$$7,\ 5,\ 6,\ 8,\ 6,\ 7,\ 5,\ 9,\ 6,\ 8,\ 7,\ 6$$
Construct a frequency table to display these results.[3 marks]
Question 3
A psychologist records the number of participants displaying three different behaviours.
Behaviour | Frequency |
Helping | \(14\) |
Ignoring | \(9\) |
Criticising | \(5\) |
Identify an appropriate graphical display for these results. Explain one reason for your choice.[2 marks]
Question 4
A researcher investigates whether background noise affects performance on a concentration task.
Condition | Mean concentration score |
Silence | \(18.5\) |
Quiet conversation | \(14.2\) |
Loud conversation | \(9.8\) |
Construct a fully labelled bar chart to display these results.[4 marks]
Question 5
The results of a memory investigation are shown below.
Number of words recalled | Frequency |
\(6\) | \(2\) |
\(7\) | \(5\) |
\(8\) | \(8\) |
\(9\) | \(4\) |
\(10\) | \(1\) |
a) Identify the most frequent recall score.[1 mark]
b) Calculate the total number of participants.[1 mark]
c) Calculate the percentage of participants who recalled \(8\) words. Show your working.[2 marks]
Question 6
Explain two differences between a bar chart and a histogram.[4 marks]
Question 7
A researcher records the time taken by \(25\) participants to complete a problem-solving task.
Completion time in seconds | Frequency |
\(0 \leq x < 10\) | \(3\) |
\(10 \leq x < 20\) | \(7\) |
\(20 \leq x < 30\) | \(9\) |
\(30 \leq x < 40\) | \(4\) |
\(40 \leq x < 50\) | \(2\) |
Construct a fully labelled histogram to display these results.[4 marks]
Question 8
A student has drawn a graph showing the frequencies of four questionnaire response categories. The bars touch, the vertical axis is not labelled and the scale increases as follows:
$$0,\ 5,\ 10,\ 20,\ 30$$
Identify three problems with the graph. For each problem, explain how it should be corrected.[6 marks]
Question 9
For each research situation below, select the most appropriate display from a table, bar chart, histogram or scattergram. Give one reason for each choice.
a) A researcher wants to show the exact mean and range for two experimental conditions.[2 marks]
b) A researcher groups participants’ response times into adjoining intervals.[2 marks]
c) A researcher wants to display the relationship between hours of sleep and memory-test scores.[2 marks]
d) A researcher wants to compare the frequencies of four attachment classifications.[2 marks]
Question 10
A researcher compares mean anxiety scores before and after a relaxation activity.
Condition | Mean anxiety score | Range |
Before relaxation | \(21.6\) | \(14\) |
After relaxation | \(13.4\) | \(8\) |
a) Calculate the difference between the two mean anxiety scores.[1 mark]
b) Describe two conclusions that can be drawn from the table. Use figures from the table in your answer.[4 marks]
c) Identify an appropriate graph for comparing the two mean anxiety scores. Explain your answer.[2 marks]
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