Sheet № 243 · Foundation + Higher · AQA · Edexcel · OCR
Stem-and-Leaf Diagrams –
Stem-and-leaf diagrams are tested on GCSE Maths papers at Foundation and Higher tier and appear across AQA, Edexcel and OCR specifications. They are a neat way to display raw data while keeping every individual value visible — unlike bar charts or histograms, no information is lost. Exam questions ask you to draw them, read off the median
§Key definitions
Question:
Draw an ordered stem-and-leaf diagram for these test scores: 34, 28, 41, 35, 29, 47, 33, 38, 42, 31, 36, 45, 27, 39, 44.
Answer:
Stem-and-leaf diagram as shown. Median = 36.
(a)
Each value appears once — there is no mode (or you could say all values are equally frequent).
(b)
Range = 47 − 27 = 20.
(c)
n = 15. Q1 position = (15 + 1) ÷ 4 = 4th value = 31. Q3 position = 3(15 + 1) ÷ 4 = 12th value = 44. IQR = 44 − 31 = 13.
§Formulas to memorise
Median position = (n + 1) ÷ 2, where n is the number of data values
Range = highest value − lowest value
Choose the stems — usually the tens digits (e.g. 1, 2, 3 for data from 10 to 39).
Write the stems — in a vertical column in ascending order.
Add the leaves — in order from smallest to largest next to the correct stem.
Write a key — e.g. "3 | 5 means 35".
To find the median — , count to the middle value using the ordered leaves.
To find the mode — , look for the most frequently occurring leaf value.
To find the range — , subtract the smallest value from the largest.
Worked example
Draw an ordered stem-and-leaf diagram for these test scores: 34, 28, 41, 35, 29, 47, 33, 38, 42, 31, 36, 45, 27, 39, 44.
Working:
⚠ Common mistakes
- ✗Unordered leaves. Leaves must be written in ascending order — an unordered diagram will lose marks.
- ✗Missing key. Without a key, the examiner cannot interpret your diagram. Always include one.
- ✗Incorrect median position. For listed data use (n + 1) ÷ 2, not n ÷ 2 (that formula is for grouped cumulative frequency).
- ✗Back-to-back errors. For the left-hand data set, leaves should increase as you move towards the stem (i.e. read from right to left).
✦ Exam tips
- →Write an unordered diagram first if that is easier, then rewrite the leaves in order — but make sure your final version is ordered.
- →For back-to-back diagrams, label which side is which clearly.
- →If asked to compare, always make one statement about an average (usually median) and one about spread (range or IQR), using the context of the data.
- →For more on averages and spread, see mean, median, mode and range. For grouped data, see frequency tables and grouped data.