Stem-and-leaf plots
Answers are for parents and teachers.
1
A café counts its customers on 14 days: 46, 38, 52, 41, 47, 38, 60, 55, 43, 38, 49, 51, 44, 58. Build an ordered plot with a key and find the median, the mode and the range.
Row 3: 8 8 8; row 4: 1 3 4 6 7 9; row 5: 1 2 5 8; row 6: 0. Key 4|6 = 46. Fourteen values: the median is (46 + 47) ÷ 2 = 46.5, the mode is 38 and the range is 60 − 38 = 22.
2
The heights of ten bean seedlings in cm: 6.4, 7.1, 5.8, 6.4, 8.0, 7.7, 6.9, 5.8, 7.1, 6.4. Plot them with the tenths as leaves, and find the median and the mode.
Row 5: 8 8; row 6: 4 4 4 9; row 7: 1 1 7; row 8: 0. Key 6|4 = 6.4 cm. The 5th and 6th values are 6.4 and 6.9: median (6.4 + 6.9) ÷ 2 = 6.65 cm. The mode is 6.4 cm (three times).
3
A plot with the key 9|3 = 93 has the rows 8 | 5 8, 9 | 0 3 3 and 10 | 2. Write the original data and find the range.
key 9|3 = 93
| Stem | Leaves |
|---|---|
| 8 | 5 8 |
| 9 | 0 3 3 |
| 10 | 2 |
85, 88, 90, 93, 93, 102. The stem 10 is the number 100 and over: 10|2 = 102. Range 102 − 85 = 17.
4
The points scored by two school teams in seven games are, team R: 16, 21, 25, 33, 36, 39, 47 and team S: 20, 24, 28, 29, 32, 35, 41. Build a back-to-back plot, then compare the medians and the ranges.
Rows 1: R 6; 2: R 5 1, S 0 4 8 9; 3: R 9 6 3, S 2 5; 4: R 7, S 1. Medians: R 33 and S 29. Ranges: R 47 − 16 = 31, S 41 − 20 = 21. Team R scores more at the centre but its scores are more spread out.
5
A pupil plots 23, 31, 25 and 47 as the rows 2 | 3 5, 3 | 1 and 4 | 7 with the key 2|3 = 2.3. What is wrong, and what should the key be?
The data are whole numbers, so each leaf is a one, not a tenth. The key should be 2|3 = 23.