Descriptive statistics: averages, tables, graphs, percentages and ratios

Measures of central tendency

• Mean: add the scores and divide by how many. Uses every score, so it is the most sensitive, but extreme scores (outliers) distort it. Use with interval/ratio data.
• Median: the middle score when the data are in order (average the two middle scores if there is an even number). Not affected by outliers. Use with ordinal data or skewed data.
• Mode: the most frequent score. The only average for nominal (category) data; there may be more than one mode or none.

Tables and graphs

• A summary table shows the descriptive statistics for each condition (mean, median, mode, range, standard deviation) side by side.
• A frequency table shows how many times each score or category occurred (often with tally marks).
• A bar chart shows separate categories or the means of conditions; bars do not touch. Use for nominal data or comparing condition means.
• A histogram shows the frequency of continuous scores in equal intervals; bars touch, the x-axis is the score and the y-axis is frequency.

All graphs need a title and labelled axes with units.

Percentages, ratios and fractions

• Percentage = part / total x 100. If 36 of 48 people said they would obey, that is 75%.
• Fraction: 36/48 simplifies to 3/4.
• Ratio: 36 obeyed : 12 refused = 3 : 1.

Pearson papers often ask for ratios and percentages from questionnaire results (June 2025 Question 3 did).

Worked example

Self-reported obedience scores for 10 males were 12, 15, 9, 14, 15, 11, 13, 15, 10, 16. Find the mean, median and mode.

1. Mean = 130 / 10 = 13.
2. In order: 9, 10, 11, 12, 13, 14, 15, 15, 15, 16; the middle two are 13 and 14, so median = 13.5.
3. Mode = 15 (it occurs three times).

Answer: Mean 13, median 13.5, mode 15.

Check yourself

1. Female obedience scores were 14, 18, 16, 13, 17, 18, 15, 12, 18, 19. Calculate the mean.
   Show answer

   16.0. 160 / 10 = 16.

2. Find the median of the female scores: 14, 18, 16, 13, 17, 18, 15, 12, 18, 19.
   Show answer

   16.5. In order: 12, 13, 14, 15, 16, 17, 18, 18, 18, 19. Middle two: 16 and 17; median = 16.5.

3. In a questionnaire, 27 of 60 participants said they would refuse an unjust order. What percentage is that?
   Show answer

   45.0 %. 27 / 60 x 100 = 45%.

4. In a survey 45 people said they would conform and 15 said they would not. What is the ratio of conformers to non-conformers in its simplest form?
   • 1 : 3
   • 3 : 1
   • 45 : 60
   • 4 : 1
   Show answer

   3 : 1. 45 : 15 = 3 : 1.

5. Which average should be used for nominal data, such as favourite type of music?
   • Mean
   • Median
   • Range
   • Mode
   Show answer

   Mode. Categories can only be counted, so use the most frequent.

6. How does a histogram differ from a bar chart?
   • Its bars are always horizontal
   • Its bars touch because it shows continuous data in equal intervals
   • It can only show percentages
   • It shows the mean of each condition
   Show answer

   Its bars touch because it shows continuous data in equal intervals. Histograms show continuous score frequencies; bar charts show separate categories.

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Sources

• Pearson Edexcel International Advanced Subsidiary/Advanced Level in Psychology specification (issue January 2026)
• Pearson International A Level Psychology component guide: WPS01
• Pearson WPS01/01 question paper, June 2025 (copy hosted by Physics and Maths Tutor)
• IAL Psychology revision site: Quantitative data

Last updated 8 November 2026. Spotted a mistake? Tell us.