Translating and presenting data | AQA A-Level Psychology Revision
- Revision Notes
- Aug 5
- 23 min read
Updated: 5 days ago
For 7182 specification, first teach in September 2025
AQA A-Level Psychology | Free Revision Notes
Estimated study time: 60 minutes
This Translating and presenting data A-Level Psychology revision page explains how psychological information can be converted between numerical, graphical and algebraic forms. You will learn how to organise raw data, select an appropriate display, plot experimental and correlational results, and interpret information presented in unfamiliar formats. These practical skills bring together work on tables and graphs, statistical equations and research design. They may be assessed through calculations, graph construction, data interpretation or application to an unfamiliar investigation.
Learning Objectives 🎯
By the end of this revision page, you should be able to:
Translate information between numerical, graphical and algebraic forms.
Organise raw psychological data into an appropriate table.
Select a suitable graph or diagram for a set of results.
Plot experimental data accurately.
Plot two co-variables on a scattergram.
Read numerical information from unfamiliar tables and graphs.
Interpret patterns, differences, correlations and unusual values.
Use calculations to support conclusions drawn from displayed data.
Present results clearly using suitable labels, units, scales and conventions.
Revision Notes 📚
Translating and presenting data in A-Level Psychology
Psychologists collect data in many different forms.
Results might initially appear as:
raw scores on a record sheet;
frequencies within categories;
ratings from a questionnaire;
paired scores from a correlation;
means and standard deviations;
observed and expected frequencies;
algebraic equations;
graphs or diagrams.
Researchers must be able to organise, translate and present these results so that patterns can be identified and communicated clearly.
AQA requires students to be able to:
translate information between graphical, numerical and algebraic forms;
plot two variables from experimental or other data;
construct and interpret frequency tables and diagrams;
construct and interpret bar charts and histograms;
use scatter diagrams to identify correlations;
interpret psychological data presented in unfamiliar formats.
Three forms of information
Data may be represented in three broad forms.
Form | Description | Psychological example |
Numerical | Values, scores, frequencies or calculated statistics | Memory scores of \(8, 10, 12, 15\) |
Graphical | A visual display of values or patterns | A bar chart showing mean memory scores |
Algebraic | Symbols and equations representing mathematical relationships | \(\bar{x}=\frac{\sum x}{N}\) |
Translation involves changing information from one form into another while preserving its meaning.
For example:
$$\text{Raw scores}\rightarrow\text{Frequency table}\rightarrow\text{Bar chart}$$
or:
$$\text{Equation}\rightarrow\text{Numerical substitution}\rightarrow\text{Calculated result}$$
Why psychologists translate data
Translating information can help a researcher:
reduce a large set of results into a manageable form;
identify patterns that are difficult to see in raw data;
compare conditions or groups;
examine the relationship between co-variables;
calculate descriptive or inferential statistics;
communicate findings to other researchers;
check whether a conclusion is supported by the data.
Different formats highlight different aspects of the same results.
A table may provide precise values, while a graph may make a pattern easier to see quickly.
Numerical data
Raw numerical data
Raw data are the original results collected before they have been organised or summarised.
Suppose participants recall the following numbers of words:
$$8,\ 10,\ 9,\ 12,\ 10,\ 11,\ 8,\ 10,\ 13,\ 9$$
These scores provide detailed information about individual performance, but the overall pattern may not be immediately obvious.
The data can be translated into a frequency table.
Translating raw scores into a frequency table
Count how many times each score occurs.
Words recalled | Frequency |
\(8\) | \(2\) |
\(9\) | \(2\) |
\(10\) | \(3\) |
\(11\) | \(1\) |
\(12\) | \(1\) |
\(13\) | \(1\) |
Check the total frequency:
$$2+2+3+1+1+1=10$$
This matches the original number of scores.
The frequency table makes it easier to see that the most frequently occurring score is:
$$10$$
Translating raw data into summary statistics
The same scores can be summarised using measures of central tendency and dispersion.
For example:
$$\text{Mean}=\frac{\sum x}{N}$$
Add the scores:
$$8+10+9+12+10+11+8+10+13+9=100$$
There are:
$$N=10$$
scores.
Therefore:
$$\bar{x}=\frac{100}{10}=10$$
The mean number of words recalled is:
$$\boxed{10}$$
The calculation and selection of averages are covered in measures of central tendency.
Frequencies and percentages
Frequencies may be converted into percentages to show the proportion of a sample falling into each category.
Use:
$$\text{Percentage}=\frac{\text{Frequency}}{\text{Total}}\times100$$
In the memory example, \(3\) out of \(10\) participants recalled exactly \(10\) words.
Therefore:
$$\text{Percentage}=\frac{3}{10}\times100$$
$$\boxed{\text{Percentage}=30\%}$$
Percentages are particularly useful when comparing groups with different sample sizes. These calculations are developed in percentages, ratios and numerical data.
Graphical data
What is a graphical display?
A graphical display represents results visually.
A suitable display may help a reader identify:
differences between conditions;
the most frequent category;
trends across ordered values;
the shape of a distribution;
the relationship between two co-variables;
unusual scores;
similarities and differences between groups.
Displays required within the AQA Research Methods content include:
tables;
bar charts;
histograms;
scattergrams;
other suitable graphs and diagrams.
Selecting an appropriate display
The type of data and purpose of the display determine which form should be used.
Data or purpose | Suitable presentation |
Frequencies for separate categories | Bar chart |
Continuous numerical data grouped into intervals | Histogram |
Relationship between two co-variables | Scattergram |
Exact numerical values | Table |
Summary statistics for conditions | Table or suitable graph |
Proportions forming a complete total | Pie chart may be suitable |
Do not select a display simply because it is familiar. It must match the structure of the data.
Presenting data in tables
Features of an effective table
A clear table should include:
an informative title;
labelled rows and columns;
units where appropriate;
consistent decimal places;
values arranged logically;
totals where they are helpful;
enough information for the reader to understand the results.
Example experimental-results table
A psychologist compares memory performance in two conditions.
Condition | Mean words recalled | Standard deviation |
Silence | \(16.4\) | \(2.1\) |
Background speech | \(12.8\) | \(4.6\) |
The table allows the reader to compare both:
average performance;
variation within each condition.
Interpreting the table
The silence condition has the higher mean:
$$16.4>12.8$$
The difference between the means is:
$$16.4-12.8=3.6$$
Participants recalled an average of \(3.6\) more words in silence.
The background-speech condition has the larger standard deviation:
$$4.6>2.1$$
This suggests that the scores were more widely spread in the background-speech condition.
The interpretation of spread is covered in measures of dispersion.
Raw-data tables
A raw-data table should preserve the connection between each participant and their result.
Participant | Silence score | Background-speech score |
A | \(16\) | \(12\) |
B | \(18\) | \(15\) |
C | \(15\) | \(10\) |
D | \(17\) | \(14\) |
E | \(16\) | \(13\) |
This table would be particularly useful when the same participants complete both conditions because each person’s paired scores remain on the same row.
Frequency tables
A frequency table records how often each score or category occurs.
Anxiety category | Frequency |
Low | \(9\) |
Moderate | \(15\) |
High | \(6\) |
Total | \(30\) |
This table can be translated into a bar chart.
Contingency tables
A contingency table displays frequencies for combinations of two categorical variables.
Improved | Did not improve | Total | |
Therapy | \(18\) | \(12\) | \(30\) |
No therapy | \(10\) | \(20\) | \(30\) |
Total | \(28\) | \(32\) | \(60\) |
This presentation may be used with a Chi-squared test.
Bar charts
When should a bar chart be used?
A bar chart is suitable for displaying frequencies, means or percentages for separate categories or conditions.
Examples include:
the number of participants choosing each response;
mean memory performance in two conditions;
the percentage of participants in each attachment category;
frequencies of different observed behaviours.
Features of a bar chart
A correctly constructed bar chart should have:
an informative title;
labelled axes;
units where needed;
an appropriate linear scale;
bars of equal width;
gaps between separate categories;
accurately plotted values;
a key if more than one set of data is shown.
The gaps indicate that the categories are separate rather than continuous.
Experimental variables on a bar chart
When experimental data are plotted:
the independent variable or experimental condition is usually placed on the horizontal axis;
the dependent variable is placed on the vertical axis.
For example:
Condition | Mean words recalled |
Silence | \(16.4\) |
Background speech | \(12.8\) |
The horizontal axis would show:
silence;
background speech.
The vertical axis would show:
mean number of words recalled.
Choosing a scale
A scale should:
increase in equal intervals;
cover the full range of values;
use most of the available graph area;
be easy to read;
include units where appropriate.
For data ranging from \(0\) to \(18\), a scale increasing by:
$$2$$
may be suitable:
$$0,\ 2,\ 4,\ 6,\ 8,\ 10,\ 12,\ 14,\ 16,\ 18$$
Plotting a bar chart accurately
Use this process:
Identify the categories.
Identify the value for each category.
Label the horizontal and vertical axes.
Select an equal-interval scale.
Draw bars of equal width.
Leave equal gaps between bars.
Plot each height accurately.
Add an informative title.
Check each bar against the original table.
Interpreting a bar chart
When interpreting a bar chart, identify:
the highest category;
the lowest category;
the size of any differences;
whether values are similar;
whether the graph shows frequencies, percentages or means;
whether a conclusion is supported by the displayed values.
Do not describe a difference as statistically significant unless an inferential test supports that conclusion.
A visible difference between bars is a descriptive result only.
Histograms
When should a histogram be used?
A histogram is used to display continuous numerical data divided into class intervals.
For example, response times might be grouped as:
Response time in seconds | Frequency |
\(0\text{ to }9\) | \(3\) |
\(10\text{ to }19\) | \(8\) |
\(20\text{ to }29\) | \(12\) |
\(30\text{ to }39\) | \(5\) |
\(40\text{ to }49\) | \(2\) |
The intervals form a continuous scale.
Bar chart and histogram compared
Feature | Bar chart | Histogram |
Data | Separate categories | Continuous numerical data |
Bars | Gaps between bars | Bars touch |
Horizontal axis | Category labels | Numerical scale or intervals |
Typical use | Compare categories or conditions | Show a distribution |
Order | Categories may be rearranged where appropriate | Numerical order must be preserved |
Why histogram bars touch
The bars touch because adjacent intervals are part of one continuous numerical scale.
For example:
\(10\text{ to }19\) seconds;
\(20\text{ to }29\) seconds.
The values form consecutive ranges rather than separate named categories.
Interpreting a histogram
A histogram may show:
where most scores are concentrated;
the approximate mode;
the spread of scores;
a normal distribution;
positive or negative skew;
gaps or unusual values.
The interpretation of symmetrical and skewed patterns is covered in distributions.
Scattergrams
When should a scattergram be used?
A scattergram is used to display the relationship between two co-variables.
Each point represents one participant or case and contains:
one value for the first co-variable;
one value for the second co-variable.
For example:
Participant | Hours of sleep | Memory score |
A | \(4\) | \(7\) |
B | \(5\) | \(9\) |
C | \(6\) | \(11\) |
D | \(7\) | \(14\) |
E | \(8\) | \(16\) |
The points to plot are:
$$(4,7)$$
$$(5,9)$$
$$(6,11)$$
$$(7,14)$$
$$(8,16)$$
Plotting two co-variables
To construct the scattergram:
Place one co-variable on the horizontal axis.
Place the other co-variable on the vertical axis.
Label each axis with the variable and unit.
Select a suitable scale for each axis.
Plot every pair of scores as one point.
Do not join the points.
Add an informative title.
Check that each point matches the original pair.
Why points are not joined
A scattergram does not show a sequence of connected stages.
Each point represents a separate participant or case.
Joining the points could incorrectly suggest that one observation follows another in an ordered progression.
Interpreting a scattergram
A scattergram may show:
a positive correlation;
a negative correlation;
zero correlation;
the approximate strength of the relationship;
unusual scores that do not fit the general pattern.
Positive correlation
A positive correlation occurs when higher values of one co-variable tend to be associated with higher values of the other.
The general pattern rises from left to right.
Negative correlation
A negative correlation occurs when higher values of one co-variable tend to be associated with lower values of the other.
The general pattern falls from left to right.
Zero correlation
Zero correlation occurs when there is no consistent pattern between the co-variables.
The points appear widely scattered without a clear upward or downward direction.
Strength of a correlation
The more closely the points follow a consistent pattern, the stronger the correlation.
A tight cluster around an imagined line suggests a stronger relationship.
A widely dispersed set of points suggests a weaker relationship.
The detailed interpretation of correlation coefficients is covered in scattergrams and
Correlation does not demonstrate causation
A scattergram may show that two co-variables are related.
It cannot establish:
which co-variable influences the other;
whether a third variable affects both;
that changing one variable will cause the other to change.
A graphical relationship should therefore be described as a correlation, not as proof of cause and effect.
Plotting experimental data
Experimental and correlational data compared
Experimental data | Correlational data |
Compares conditions or groups | Examines two co-variables |
Often displayed using bars or tables | Commonly displayed using a scattergram |
Includes an independent and dependent variable | Includes two measured co-variables |
May support a conclusion about a difference | Supports a conclusion about a relationship |
Worked experimental example
A psychologist investigates whether the presence of background speech affects memory.
Condition | Mean words recalled |
Silence | \(15.8\) |
Quiet instrumental music | \(14.3\) |
Background speech | \(10.9\) |
A suitable bar chart would use:
the three sound conditions on the horizontal axis;
mean words recalled on the vertical axis;
separate bars for each condition.
Interpreting the pattern
The highest mean occurred in the silence condition:
$$15.8$$
The lowest mean occurred in the background-speech condition:
$$10.9$$
The difference is:
$$15.8-10.9=4.9$$
Participants recalled an average of \(4.9\) more words in silence than with background speech.
This is a descriptive comparison. Statistical significance would require an appropriate inferential test.
Plotting individual experimental scores
Sometimes a question may require individual values rather than condition means to be plotted.
Before plotting, identify:
whether scores are continuous or categorical;
whether the display should show frequencies or individual results;
whether data have been grouped into intervals;
whether more than one condition must be shown.
Do not calculate means unless the question asks for summary values or provides a reason to use them.
Translating numerical data into graphical form
A step-by-step method
When translating a set of numerical results into a graph:
Identify what each number represents.
Determine whether the data are categorical, continuous or paired.
Decide whether the graph should show frequencies, means, percentages or individual scores.
Select the appropriate graphical form.
Organise the data into a table if needed.
Label axes clearly.
Choose a suitable scale.
Plot every value accurately.
Add a title and key where needed.
Check the graph against the original numerical information.
Example: frequency data to bar chart
Suppose an observation produces:
Behaviour | Frequency |
Cooperative | \(18\) |
Competitive | \(11\) |
Neutral | \(7\) |
Aggressive | \(4\) |
A bar chart is suitable because the behaviours form separate nominal categories.
The horizontal axis should show the behaviour categories.
The vertical axis should show frequency.
The bars should have heights of:
$$18,\ 11,\ 7,\ 4$$
with gaps between them.
Example: continuous data to histogram
Suppose reaction times are grouped into intervals.
Reaction time in milliseconds | Frequency |
\(200\text{ to }299\) | \(4\) |
\(300\text{ to }399\) | \(9\) |
\(400\text{ to }499\) | \(13\) |
\(500\text{ to }599\) | \(6\) |
A histogram is appropriate because reaction time is continuous numerical data.
The intervals must remain in numerical order, and the bars should touch.
Example: paired data to scattergram
Suppose a researcher records:
Participant | Stress rating | Sleep-quality rating |
A | \(2\) | \(8\) |
B | \(4\) | \(7\) |
C | \(5\) | \(5\) |
D | \(7\) | \(3\) |
E | \(9\) | \(2\) |
The points are:
$$(2,8)$$
$$(4,7)$$
$$(5,5)$$
$$(7,3)$$
$$(9,2)$$
These should be plotted on a scattergram.
The pattern would suggest a negative correlation because higher stress ratings tend to be associated with lower sleep-quality ratings.
Translating graphical information into numerical form
Reading values from a graph
To obtain numerical information from a graph:
Read the axis label.
Identify the unit.
Check the scale intervals.
Locate the relevant bar, point or position.
Trace carefully to the numerical axis.
Report only the precision supported by the graph.
Worked bar-chart interpretation
Suppose a graph shows mean scores of approximately:
\(18\) for Condition A;
\(13\) for Condition B.
The approximate difference is:
$$18-13=5$$
The graph suggests that Condition A produced a mean about \(5\) points higher than Condition B.
Estimating from a scale
Suppose a bar ends halfway between:
$$12$$
and:
$$14$$
A suitable estimate is:
$$13$$
Do not report:
$$13.000$$
because the graph does not support that level of precision.
Calculating a percentage from a graph
Suppose a graph shows:
\(24\) participants selected Option A;
the total sample contained \(60\) participants.
Calculate:
$$\text{Percentage}=\frac{24}{60}\times100$$
$$\boxed{\text{Percentage}=40\%}$$
The graphical frequency has been translated into a numerical percentage.
Calculating a range from a graph
Suppose a plotted data set has:
an approximate highest score of \(46\);
an approximate lowest score of \(14\).
The estimated range is:
$$46-14=32$$
The result should be identified as approximate if the exact values cannot be read from the graph.
Algebraic forms
What is algebraic information?
An algebraic form uses letters, symbols and equations to represent numerical relationships.
Examples used in psychological research include:
$$\bar{x}=\frac{\sum x}{N}$$
$$\text{Percentage}=\frac{\text{Frequency}}{\text{Total}}\times100$$
$$E=\frac{\text{Row total}\times\text{Column total}}{\text{Overall total}}$$
$$df=(r-1)(c-1)$$
The symbols represent quantities that can be replaced with numerical values.
Translating an equation into words
Consider:
$$\bar{x}=\frac{\sum x}{N}$$
This can be translated into words as:
The mean equals the total of the scores divided by the number of scores.
For:
$$df=(r-1)(c-1)$$
the verbal translation is:
Degrees of freedom equal one less than the number of rows multiplied by one less than the number of columns.
Understanding the meaning of the symbols helps prevent incorrect substitution.
Translating numerical information into an equation
Suppose:
the total of the scores is \(360\);
the number of scores is \(20\).
Translate this information into the mean equation:
$$\bar{x}=\frac{360}{20}$$
Calculate:
$$\boxed{\bar{x}=18}$$
Translating a frequency problem into algebraic form
Suppose \(21\) out of \(70\) participants selected a response.
Use:
$$\text{Percentage}=\frac{\text{Frequency}}{\text{Total}}\times100$$
Substitute:
$$\text{Percentage}=\frac{21}{70}\times100$$
Calculate:
$$\boxed{\text{Percentage}=30\%}$$
The numerical information has been represented algebraically and then solved.
Translating table information into an equation
Suppose a Chi-squared contingency table gives:
relevant row total: \(40\);
relevant column total: \(24\);
overall total: \(60\).
Use:
$$E=\frac{\text{Row total}\times\text{Column total}}{\text{Overall total}}$$
Substitute:
$$E=\frac{40\times24}{60}$$
Calculate:
$$E=\frac{960}{60}$$
$$\boxed{E=16}$$
This is the expected frequency for the relevant cell.
Translating algebraic results into psychological conclusions
A calculation should often be followed by a contextual statement.
For example:
$$\bar{x}=18$$
becomes:
Participants recalled a mean of \(18\) words.
The result:
$$E=16$$
becomes:
If there were no association between the variables, \(16\) participants would be expected in this category combination.
The result:
$$df=2$$
becomes:
The researcher should use the row for \(df=2\) in the relevant critical-values table.
The practical use of equations is covered in mathematical skills in Psychology.
Interpreting unfamiliar formats
What makes a format unfamiliar?
An examination question may present familiar information in a format you have not practised directly.
For example:
a table arranged in an unusual direction;
a graph with two vertical scales;
data embedded in a research scenario;
values expressed in standard form;
a chart containing percentages rather than frequencies;
a set of paired scores without explicit coordinate notation;
a graph showing error bars;
a diagram combining several statistics.
You should not rely only on recognising the appearance of a familiar textbook example.
Instead, work out what each part of the display represents.
A systematic interpretation method
Use the following sequence.
Step 1: Read the title
The title should indicate:
what was measured;
which groups or conditions are shown;
the context of the investigation.
Step 2: Identify the variables
Ask:
What is the independent variable?
What is the dependent variable?
Are there two co-variables?
Are the data categories, ratings or numerical measurements?
Step 3: Read all labels
Check:
row headings;
column headings;
horizontal-axis labels;
vertical-axis labels;
units;
keys;
annotations.
Step 4: Examine the scale
Check whether:
intervals are equal;
the scale starts at zero;
values are shown as frequencies, percentages or means;
different axes use different units;
values have been multiplied by a factor.
Step 5: Identify the overall pattern
Look for:
the highest and lowest values;
differences between conditions;
upward or downward trends;
clusters;
skew;
correlations;
unusual scores;
changes over time or order.
Step 6: Use numerical evidence
Support the interpretation with values.
Instead of writing:
Condition A was better.
Write:
Condition A produced a mean score of \(18\), compared with \(13\) in Condition B, a difference of \(5\) points.
Step 7: Avoid unsupported conclusions
Do not claim:
statistical significance without a statistical test;
causation from a correlation;
generalisation beyond the evidence;
precise values that cannot be read from the display.
Interpreting a display with percentages
Suppose a chart shows:
Response | Group A | Group B |
Agreed | \(60\%\) | \(45\%\) |
Disagreed | \(40\%\) | \(55\%\) |
The percentage-point difference in agreement is:
$$60-45=15$$
Group A has a \(15\) percentage-point higher agreement rate.
Do not describe this as:
$$15\%$$
more without considering whether the question requires percentage points or percentage change.
Frequencies and unequal samples
Suppose:
\(30\) participants in Group A choose an option out of \(50\);
\(36\) participants in Group B choose the same option out of \(80\).
The raw frequency is higher in Group B:
$$36>30$$
However, the percentages are:
$$\frac{30}{50}\times100=60\%$$
and:
$$\frac{36}{80}\times100=45\%$$
A larger proportion of Group A chose the option.
This shows why frequencies can be misleading when groups have different sizes.
Interpreting two summary statistics
Suppose a display reports:
Condition | Mean | Standard deviation |
A | \(20.4\) | \(2.2\) |
B | \(18.9\) | \(6.8\) |
Condition A has the higher mean:
$$20.4>18.9$$
Condition B has the greater dispersion:
$$6.8>2.2$$
A suitable interpretation is:
Participants in Condition A achieved a slightly higher average score, while scores in Condition B were considerably more variable.
Do not focus only on the means when information about spread is also provided.
Interpreting unusual values
An unusual value may be:
far from the other scores;
separated from a cluster;
inconsistent with the general correlational pattern;
much higher or lower than surrounding values.
An unusual score may affect:
the mean;
the range;
standard deviation;
the appearance of a scattergram;
the apparent strength of a correlation.
Do not automatically remove an unusual value. The researcher would need a justified reason for excluding data.
Accuracy when presenting data
Labels
Every display should identify:
the variable;
the unit;
the conditions or categories;
what each value represents.
A label such as:
Score
may be too vague.
A clearer label is:
Mean number of words recalled
Units
Possible units include:
seconds;
milliseconds;
centimetres;
words recalled;
errors;
participants;
percentage;
rating-scale points.
Do not combine values measured in different units without converting them first.
Scales
A scale should use equal intervals.
For example:
$$0,\ 5,\ 10,\ 15,\ 20$$
is an equal-interval scale.
The following is misleading:
$$0,\ 5,\ 10,\ 50,\ 55$$
if the gaps are displayed as though they are equal.
Precision
Use only the precision supported by the data.
If values are given to one decimal place, it may be appropriate to present calculated means consistently.
For example:
$$12.4,\ 15.8,\ 16.1$$
A displayed mean of:
$$14.766666\ldots$$
should normally be rounded appropriately rather than reported with unnecessary digits.
Significant figures
Correlation coefficients should be reported using an appropriate number of significant figures, such as two or three.
For example:
$$r_s=-0.73642\ldots$$
to three significant figures becomes:
$$\boxed{r_s=-0.736}$$
Titles
A good title identifies both the measure and the comparison.
Weak title:
Results
Stronger title:
Mean number of words recalled in each background-sound condition
Keys and legends
A key is needed when:
more than one group is displayed;
different symbols represent different categories;
several lines or sets of bars appear on the same graph.
The key should clearly identify each group or condition.
Comparing data displays
Tables and graphs have different strengths
Tables | Graphs |
Show precise values | Make broad patterns easy to see |
Allow exact calculations | Make comparisons visually immediate |
Can include several statistics | May reduce numerical detail |
Useful for checking individual results | Useful for identifying trends and unusual values |
A researcher may use both forms because they communicate different aspects of the results.
Choosing between raw and summary data
Raw data preserve individual scores.
Summary data reduce the scores to statistics such as:
mean;
median;
mode;
range;
standard deviation;
percentage.
Summary values make comparisons easier but remove some information about individual participants.
A graph of condition means, for example, does not show every participant’s result.
Selecting the best format
Ask what the reader needs to understand.
Use a table when:
exact values are important;
several statistics must be compared;
individual results must remain visible.
Use a graph when:
the overall pattern is more important;
conditions need to be compared quickly;
a distribution must be shown;
a correlation must be identified.
Complete worked example: experimental data
Research scenario
A psychologist investigates whether background sound affects the number of words recalled.
The results are:
Participant | Silence | Instrumental music | Speech |
A | \(16\) | \(14\) | \(10\) |
B | \(18\) | \(15\) | \(12\) |
C | \(15\) | \(13\) | \(11\) |
D | \(17\) | \(16\) | \(9\) |
E | \(14\) | \(12\) | \(8\) |
Translate raw scores into means
Silence
$$\bar{x}=\frac{16+18+15+17+14}{5}$$
$$\bar{x}=\frac{80}{5}$$
$$\bar{x}=16$$
Instrumental music
$$\bar{x}=\frac{14+15+13+16+12}{5}$$
$$\bar{x}=\frac{70}{5}$$
$$\bar{x}=14$$
Speech
$$\bar{x}=\frac{10+12+11+9+8}{5}$$
$$\bar{x}=\frac{50}{5}$$
$$\bar{x}=10$$
Present the summary numerically
Condition | Mean words recalled |
Silence | \(16\) |
Instrumental music | \(14\) |
Speech | \(10\) |
Select a graphical form
A bar chart is suitable because:
the independent variable contains separate sound conditions;
the dependent variable is the mean number of words recalled;
the purpose is to compare the conditions.
Interpret the display
The silence condition produced the highest mean:
$$16$$
The speech condition produced the lowest mean:
$$10$$
The difference is:
$$16-10=6$$
Participants recalled an average of \(6\) more words in silence than with speech.
The graph would show a descriptive difference. An inferential test would be required to decide whether it was statistically significant.
Complete worked example: correlational data
Research scenario
A researcher investigates whether sleep duration is related to memory performance.
Participant | Sleep in hours | Memory score |
A | \(4\) | \(7\) |
B | \(5\) | \(8\) |
C | \(6\) | \(11\) |
D | \(7\) | \(13\) |
E | \(8\) | \(15\) |
F | \(9\) | \(16\) |
Translate the table into coordinates
$$(4,7)$$
$$(5,8)$$
$$(6,11)$$
$$(7,13)$$
$$(8,15)$$
$$(9,16)$$
Select a graphical form
A scattergram is appropriate because:
two co-variables have been measured;
each participant provides a paired score;
the researcher is investigating a correlation.
Plot the variables
The horizontal axis could show:
Sleep duration in hours
The vertical axis could show:
Memory-test score
Each coordinate should be plotted once, and the points should not be joined.
Interpret the pattern
The points would show an upward pattern.
This suggests a positive correlation:
Participants who slept for longer tended to achieve higher memory scores.
The graph does not establish that additional sleep caused better memory performance.
A checklist for constructing a graph
Before drawing:
Have I identified the data type?
Have I selected the correct display?
Do I know what each value represents?
While drawing:
Is there an informative title?
Are both axes labelled?
Are units included?
Does the scale use equal intervals?
Have I used most of the available space?
Are bar widths consistent?
Are gaps used appropriately?
Have all points or values been plotted?
Is a key needed?
After drawing:
Do plotted values match the source data?
Are categories in the correct order?
Is the graph easy to interpret?
Have I avoided adding unsupported information?
A checklist for interpreting unfamiliar data
Use the following process:
Identify the research question.
Identify the variables.
Identify the type and level of data.
Read the title, labels, units and key.
Check the scale.
Identify the highest and lowest values.
Calculate relevant differences or percentages.
Look for trends, correlations or unusual values.
Consider both central tendency and dispersion where provided.
Use numerical evidence in the answer.
Distinguish descriptive differences from statistical significance.
Avoid claiming causation from correlational information.
Key Words 🔑
Key word | Student-friendly definition | How it may be used in an exam |
Numerical form | Information presented as values, scores, frequencies or statistics. | You may translate numerical results into a table, equation or graph. |
Graphical form | Information displayed visually using a graph or diagram. | You may construct or interpret a bar chart, histogram or scattergram. |
Algebraic form | Information represented using symbols and equations. | You may substitute psychological data into an equation. |
Raw data | Original results before they have been organised or summarised. | You may organise raw scores into a table or calculate summary statistics. |
Frequency | The number of times a score, behaviour or category occurs. | Frequencies may be shown in a table, bar chart or contingency table. |
Frequency table | A table recording how often each value or category occurs. | You may construct one from raw data. |
Bar chart | A display using separated bars to compare categories, conditions or values. | You may select or draw one for categorical experimental data. |
Histogram | A display using adjoining bars for continuous data grouped into intervals. | You may use one to examine the shape of a distribution. |
Scattergram | A graph displaying paired scores for two co-variables. | You may plot points and identify a positive, negative or zero correlation. |
Contingency table | A table showing frequencies for combinations of two categorical variables. | It may be used with a Chi-squared test. |
Scale | The numerical progression used on an axis. | A scale should use equal intervals and cover the data range. |
Axis | A reference line on a graph showing a variable and its values. | Both axes should be clearly labelled and include units where needed. |
Key | An explanation of symbols, patterns or data sets within a graph. | It is required when more than one group or category is represented. |
Co-variable | One of the two measured variables in a correlation. | Co-variable pairs are plotted on a scattergram. |
Coordinate | A paired horizontal and vertical value plotted as one point. | Each participant’s co-variable scores form one coordinate. |
Correlation | A relationship between two co-variables. | A scattergram may show its direction and approximate strength. |
Trend | A general pattern of change across a data display. | You may describe an upward, downward or absent pattern. |
Unusual value | A score that lies apart from most other observations. | It may affect the apparent pattern or descriptive statistics. |
Estimate | An approximate value obtained from rounded or graphical information. | You may estimate a value, range or difference from a display. |
Summary statistic | A calculated value used to describe a data set. | Examples include the mean, median, range and standard deviation. |
Hints from the Examiner Reports 💡
No lesson-specific examiner guidance was identified in the provided reports.
Common Mistakes ⚠️
Mistake: Selecting a bar chart for a correlation.
Why this is incorrect:
A correlation involves paired values for two co-variables and should normally be displayed using a scattergram.
How to improve:
Ask whether each participant provides one score or a pair of co-variable scores.
Mistake: Joining the points on a scattergram.
Why this is incorrect:
Each point represents a separate participant or case rather than a stage in an ordered sequence.
How to improve:
Plot each coordinate independently and leave the points unconnected.
Mistake: Reversing scores when plotting coordinates.
Why this is incorrect:
If the first co-variable is on the horizontal axis, its value must be plotted first for every coordinate.
How to improve:
Write the axis order above the data:
$$(x,y)=(\text{horizontal value},\text{vertical value})$$
Mistake: Using gaps between histogram bars.
Why this is incorrect:
A histogram represents continuous numerical intervals.
How to improve:
Use adjoining bars for continuous grouped data.
Mistake: Allowing bar-chart bars to touch.
Why this is incorrect:
Separate categories are not parts of one continuous scale.
How to improve:
Leave equal gaps between the bars.
Mistake: Using an uneven axis scale.
Why this is incorrect:
Equal visual distances must represent equal numerical differences.
How to improve:
Choose a consistent interval and check every axis label.
Mistake: Omitting axis labels or units.
Why this is incorrect:
The reader cannot identify what the displayed values represent.
How to improve:
Name the variable fully and add units such as seconds, words or percentages.
Mistake: Using a title such as “Results”.
Why this is incorrect:
The title does not identify the variables or comparison.
How to improve:
State what is measured and across which conditions or variables.
Mistake: Plotting values that were not requested.
Why this is incorrect:
A question may ask for raw scores, frequencies, percentages or means. These are not interchangeable.
How to improve:
Identify exactly what the vertical axis should represent before calculating or plotting.
Mistake: Confusing frequencies with percentages.
Why this is incorrect:
A frequency is a count, while a percentage expresses a proportion of the total.
How to improve:
Check the table heading, axis label and sample size before interpreting a value.
Mistake: Comparing frequencies from groups of different sizes.
Why this is incorrect:
A larger group may produce a higher frequency even when a smaller proportion selected the response.
How to improve:
Convert frequencies into percentages before comparing unequal groups.
Mistake: Describing a visible difference as statistically significant.
Why this is incorrect:
A graph or table provides descriptive information only.
How to improve:
Use the term statistically significant only when an inferential test supports it.
Mistake: Claiming causation from a scattergram.
Why this is incorrect:
A scattergram shows a relationship but cannot establish the direction of causality or eliminate third variables.
How to improve:
Use phrases such as correlated with, related to or associated with.
Mistake: Ignoring standard deviation when it is provided.
Why this is incorrect:
Means describe average performance, while standard deviations provide information about the spread of scores.
How to improve:
Compare both central tendency and dispersion.
Mistake: Reporting more precision than the graph supports.
Why this is incorrect:
A graph may allow only an approximate reading.
How to improve:
Use reasonable precision and state that a value is approximate where necessary.
Mistake: Failing to use numerical evidence.
Why this is incorrect:
A statement such as “Condition A was better” does not show how the interpretation was reached.
How to improve:
Quote relevant values and calculate a difference where appropriate.
Mistake: Misreading an unfamiliar orientation.
Why this is incorrect:
A table may place conditions in rows rather than columns, or reverse the expected axes.
How to improve:
Read every heading and label before interpreting the values.
Exam-Style Questions ✍️
Question 1
The following memory scores were recorded:
$$6,\ 8,\ 7,\ 8,\ 9,\ 6,\ 8,\ 10,\ 7,\ 8$$
Construct a frequency table showing each score and its frequency.[3 marks]
Question 2
A researcher records the following frequencies:
Response category | Frequency |
Agree | \(18\) |
Neither agree nor disagree | \(9\) |
Disagree | \(13\) |
State an appropriate graphical display for these data. Explain your choice.[2 marks]
Question 3
A psychologist records participants’ response times in the following intervals:
Response time in milliseconds | Frequency |
\(200\text{ to }299\) | \(4\) |
\(300\text{ to }399\) | \(11\) |
\(400\text{ to }499\) | \(15\) |
\(500\text{ to }599\) | \(6\) |
State an appropriate graphical display and explain how the bars should be presented.[3 marks]
Question 4
A researcher compares mean memory performance in three conditions.
Condition | Mean words recalled |
Silence | \(17.2\) |
Instrumental music | \(14.8\) |
Speech | \(11.3\) |
Sketch an appropriate graph to display the results. Include:
an informative title;
labelled axes;
an appropriate scale;
accurately plotted values.
[5 marks]
Question 5
Using the data in Question 4, calculate the difference between the highest and lowest condition means. Interpret the result in context.[2 marks]
Question 6
A psychologist investigates whether sleep duration is related to concentration score.
Participant | Sleep in hours | Concentration score |
A | \(4\) | \(6\) |
B | \(5\) | \(8\) |
C | \(6\) | \(9\) |
D | \(7\) | \(12\) |
E | \(8\) | \(14\) |
F | \(9\) | \(15\) |
a) State an appropriate graphical display.[1 mark]
b) List the six coordinates that should be plotted.[2 marks]
c) Describe the likely relationship shown by the completed display.[2 marks]
Question 7
A student joins all the points on a scattergram with straight lines.
Explain why this is inappropriate.[2 marks]
Question 8
The mean and standard deviation for two conditions are shown below.
Condition | Mean score | Standard deviation |
A | \(24.6\) | \(2.3\) |
B | \(22.9\) | \(7.1\) |
Compare the results of the two conditions. Refer to both average performance and dispersion.[4 marks]
Question 9
In Group A, \(30\) out of \(50\) participants select Option 1.
In Group B, \(36\) out of \(80\) participants select Option 1.
a) Calculate the percentage selecting Option 1 in each group.[2 marks]
b) Explain why comparing the raw frequencies alone could be misleading.[2 marks]
Question 10
A graph shows that approximately \(42\) participants selected Response A and approximately \(18\) selected Response B.
Estimate:
a) the total number of participants;[1 mark]
b) the percentage selecting Response A.[2 marks]
Question 11
The following equation is used to calculate a mean:
$$\bar{x}=\frac{\sum x}{N}$$
A study has a total score of:
$$468$$
from:
$$N=24$$
participants.
a) Substitute the values into the equation.[1 mark]
b) Calculate the mean.[1 mark]
c) State what the result would represent if the variable was the number of words recalled.[1 mark]
Question 12
For one cell in a contingency table:
$$\text{Row total}=36$$
$$\text{Column total}=25$$
$$\text{Overall total}=60$$
Translate these numerical values into the expected-frequency equation and calculate \(E\).
Use:
$$E=\frac{\text{Row total}\times\text{Column total}}{\text{Overall total}}$$
[3 marks]
Question 13
A bar chart appears to show that participants performed better in Condition A than Condition B.
Explain why the researcher cannot conclude from the bar chart alone that the difference is statistically significant.[3 marks]
Question 14
A scattergram shows a strong negative relationship between stress scores and sleep-quality scores.
Explain:
a) what the negative pattern means;[2 marks]
b) why the graph cannot show that stress caused poor sleep quality.[2 marks]
Question 15
An unfamiliar graph displays:
condition means on the vertical axis;
conditions on the horizontal axis;
error bars around each mean;
different patterns for two participant groups.
Describe four features a student should check before interpreting the graph.[4 marks]
Question 16
A psychologist records raw scores from two experimental conditions and paired scores from a separate correlational investigation.
Explain which graphical display should be used for:
a) comparing the experimental conditions;[2 marks]
b) displaying the correlational results.[2 marks]
Justify each choice.
Comments