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Learn8300Papers 1–3 · Higher tierStatisticsCollecting data and stem-and-leaf diagrams
Statistics · Subtopic 1 of 5

Collecting Data and Stem-and-Leaf Diagrams

Data is qualitative (words) or quantitative (numbers); numbers are discrete (counted) or continuous (measured). A fair sample represents the whole population without bias. Frequency tables and stem-and-leaf diagrams organise raw data so you can read off the median, mode and range.

Cambridge 4024 Paper 1Cambridge 4024 Paper 2Edexcel 4MA1 Papers 1H, 2HEdexcel 4MA1 Papers 1F, 2FAQA 8300 Papers 1–3≈ 25 minRevision 5 · updated 2026-10-27
Section 1 of 14

Learning objectives

  • Classify data as qualitative or quantitative, discrete or continuous.
  • Recognise biased samples and questions.
  • Build and read frequency tables and grouped tables.
  • Draw and interpret ordered stem-and-leaf diagrams with a key.
Pause and think

To find out how much exercise people do, you ask 5050 people leaving a gym. What's wrong with this sample?

Section 2 of 14

Core idea

Start hereA table that is also a chart

A stem-and-leaf diagram lists every value in order and shows the shape of the data, like a bar chart turned on its side. Nothing is lost, so medians and ranges can be read straight off.

The big idea

Ordered leaves with a key. Median position n+12\frac{n+1}2. Data types: qualitative/quantitative; discrete/continuous.

1. Reading a stem-and-leaf

Stem-and-leaf: times (seconds) of 12 runners
112 5 8120 3 3 7 9131 4146Key: 12 | 3 = 12.3 smedian = 12.5 s
The 6th and 7th values are 12.3 and 12.7, so the median is 12.5 s. The range is 14.6−11.2=3.414.6-11.2=3.4 s.
Worked example12 runners

Median and range from the diagram.

Goal
Two values.
Strategy
Position 12+12=6.5\frac{12+1}2=6.5.
  1. 6th and 7th values→12.5\text{6th and 7th values}\to12.5
    Average of the two middle values.
  2. 14.6−11.2=3.414.6-11.2=3.4
    Largest − smallest.
AnswerMedian 12.512.5 s; range 3.43.4 s.
✓ CheckMedian lies between the extremes ✓.
  • Qualitative (words) vs quantitative (numbers).
  • Discrete (counted) vs continuous (measured).
Common misconceptionMissing key Without "11 | 2 means 11.2 s", the diagram is ambiguous.
Pause and think

Is shoe size discrete or continuous?

Summary

  • Ordered leaves with a key.
  • Read median and range directly.
Key words
Discrete
Only certain values.
Continuous
Any value in a range.
HistoryThe Domesday Book. In 10861086 William the Conqueror ordered a survey of every landholding in England: the Domesday Book. Officials recorded 13 41813\,418 places, down to the number of pigs. It's one of the earliest large-scale data collections, and it's still in the National Archives.
Fun factThe poll of 2.4 million that got it wrong. In 19361936 the Literary Digest polled 2.42.4 million Americans and predicted Alf Landon would beat Franklin Roosevelt easily. Roosevelt won 4646 of 4848 states. The sample came from telephone and car owners: wealthier people. A huge biased sample is still biased.
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