Sheet № 64 · Foundation + Higher · AQA · Edexcel · OCR
Frequency Tables and Grouped Data –
Frequency tables and grouped data are core statistics skills tested across AQA, Edexcel and OCR GCSE Maths papers. At Foundation level you need to read and interpret simple frequency tables; at Higher level you must estimate the mean from grouped data, identify the modal class and find the class interval containing the median. These skill
§Key definitions
Question:
The table shows the shoe sizes of 20 pupils.
(a) Mode:
The highest frequency is 7, which corresponds to shoe size 6. Mode = 6.
(c) Median:
n = 20. Position = (20 + 1) ÷ 2 = 10.5th value, so the median is the mean of the 10th and 11th values. Cumulative frequencies: 2, 7, 14, 18, 20. The 10th and 11th values both fall in the shoe size 6 group (positions 8–14). Median = 6.
(a) Modal class:
The highest frequency is 14, so the modal class is 30 ≤ t < 40.
(c) Median class:
n = 40, so the median is between the 20th and 21st values. Cumulative frequencies: 3, 12, 26, 36, 40. The 20th and 21st values both fall in the 30 ≤ t < 40 class.
§Formulas to memorise
Class interval — the range each group covers (e.g. 20–39).
Class width — the difference between the upper and lower boundaries of a class.
Midpoint — the middle value of a class interval, found by adding the endpoints and dividing by two.
Modal class — the class interval with the highest frequency.
Worked example
The table shows the shoe sizes of 20 pupils. | Shoe size | 4 | 5 | 6 | 7 | 8 | |---|---|---|---|---|---| | Frequency | 2 | 5 | 7 | 4 | 2 | (a) Find the mode. (b) Calculate the mean shoe size. (c) Find the median shoe size.
Working:
⚠ Common mistakes
- ✗Using end values instead of midpoints when estimating the mean from grouped data. Always add the class boundaries and divide by two.
- ✗Giving a single value for the modal class — write the full class interval, e.g. "30 ≤ t < 40", not "35".
- ✗Forgetting to say "estimate" — when the data is grouped, the mean is an estimate. Examiners expect this word.
- ✗Misreading class boundaries — pay attention to whether the table uses discrete classes (e.g. 0–9, 10–19) or continuous classes (e.g. 0 ≤ x < 10). This affects the midpoint calculation.
- ✗Dividing by the number of classes instead of the total frequency.
✦ Exam tips
- →Set out your working in a table — add columns for midpoints and midpoint × frequency. This keeps your arithmetic organised and earns method marks.
- →Label your answer clearly — write "Estimated mean = …" for grouped data.
- →Cumulative frequency column — add one when you need to find the median class or draw a cumulative frequency graph. This links to cumulative frequency and box plots.
- →Cross-check totals — quickly verify that your frequency total matches the number of data items stated in the question.
- →Review key formulas on our GCSE Maths formulas page.