MathematicsExam 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
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