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

The key is part of the diagram and carries a mark of its own — the syllabus requires ordered data and a key, and "key" appears in 14 of the 43 papers. Write it out in full, for example 3 | 7 means 37, and put the leaves in order within each row.

Worked example

Reading a median off the leaves

A stem-and-leaf diagram shows ten values: stem 2 with leaves 3 and 5; stem 3 with leaves 1, 4, 4 and 8; stem 4 with leaves 2, 5 and 7; stem 5 with leaf 1. The key states 2 | 3 represents 23. Find the median and the range.

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