Quartiles of lists and stem-and-leaf plots
Answers are for parents and teachers.
1
A bakery sells these numbers of loaves on 13 days: 64, 58, 71, 49, 80, 66, 53, 75, 60, 69, 57, 62, 73. Find Q₁, Q₂ and Q₃.
Ordered: 49, 53, 57, 58, 60, 62, 64, 66, 69, 71, 73, 75, 80. n + 1 = 14: places 3.5, 7, 10.5. Q₁ = 57 + 0.5 × 1 = 57.5, Q₂ = 64, Q₃ = 71 + 0.5 × 2 = 72.
2
Fifteen paper planes fly these distances in metres: 27, 35, 31, 22, 40, 29, 36, 25, 33, 38, 24, 30, 28, 41, 34. Find the three quartiles. Why is no rule between two values needed?
Ordered: 22, 24, 25, 27, 28, 29, 30, 31, 33, 34, 35, 36, 38, 40, 41. n + 1 = 16: places 4, 8, 12, all whole numbers, so the quartiles are data values: Q₁ = 27, Q₂ = 31, Q₃ = 36 m.
3
The plot shows 12 invented marks. Find Q₁, Q₂ and Q₃.
key 3|2 = 32
| Stem | Leaves |
|---|---|
| 3 | 0 2 5 6 8 |
| 4 | 1 3 4 5 7 9 |
| 5 | 2 |
n + 1 = 13: places 3.25, 6.5, 9.75. Values: 30, 32, 35, 36, 38, 41, 43, 44, 45, 47, 49, 52. Q₁ = 35 + 0.25 × 1 = 35.25; Q₂ = 41 + 0.5 × 2 = 42; Q₃ = 45 + 0.75 × 2 = 46.5.
4
Find the quartiles of the five values 5, 8, 9, 12, 20.
n + 1 = 6: places 1.5, 3 and 4.5. Q₁ = 5 + 0.5 × 3 = 6.5; Q₂ = 9; Q₃ = 12 + 0.5 × 8 = 16.
5
A set of 40 values has Q₁ = 12.5 and Q₃ = 21. About how many values lie between Q₁ and Q₃? Explain.
About 20: a quarter of the values are before Q₁ and a quarter after Q₃, so half of the 40 values lie between them.