Mathematics (Core)Exam code: 0580
Statistical Diagrams
Statistics
Structure and key
- A stem-and-leaf diagram displays the actual data values while also showing their shape
- Each value splits into a stem, usually the tens digit, and a leaf, usually the units digit
- The syllabus requires the data to be ordered and the diagram to carry a key
- The key states what a particular stem and leaf combination represents, including units, such as 2 | 3 represents 23 g
- Other splits are possible, so a key might make 2 | 3 mean 2.3 or 2300, and reading it is essential
Using one
- Because every value is still visible, the median, mode and range can all be read off directly
- Count the leaves in order to find the median position, working along the rows from the top
- The range is the largest value minus the smallest, both of which sit at the ends
- Questions also run backwards, giving the median, mean or range and asking for missing leaves
Exam tip
Put the leaves in order
Completing a stem-and-leaf diagram from a list is worth two marks, and a diagram with every value in its right row but the leaves out of order earns only one. So draft it first: go along the list once, writing each leaf beside its stem and crossing the value off, then copy each row into the diagram with its leaves from smallest to largest. Count the leaves: one for every value in the list.
Worked example
Reading a median off the leaves
The stem-and-leaf diagram shows ten values. Find the median and the range.
| Stem | Leaf |
|---|---|
| 2 | 3 5 |
| 3 | 1 4 4 8 |
| 4 | 2 5 7 |
| 5 | 1 |
Key: 2 | 3 represents 23
Solution:
- The values in order are 23, 25, 31, 34, 34, 38, 42, 45, 47, 51
- There are 10 values, an even number, so the median is midway between the 5th and 6th
- The 5th value is 34 and the 6th is 38
- Median = (34 + 38) ÷ 2 = 36
- The range is the largest minus the smallest: 51 − 23 = 28