Histograms and cumulative frequency graphs Problem set A Answers

1. (a) Bars of heights 4, 9, 15, 8, 4 (the frequencies), touching, on a horizontal axis from 0 to 25.
2. (b) Frequency densities 2, 3, 2.4, 1.05. Bars of width 5, 5, 10, 20.

1. (a) 11
2. (b) 26

1. (a) 3, 10, 24, 34, 40
2. (b) Points (20, 0), (25, 3), (30, 10), (35, 24), (40, 34), (45, 40) joined in order; the graph ends at (45, 40).

1. (a) 24 g
2. (b) 16 g
3. (c) 46 g
4. (d) 17
5. (e) 16%

1. (a) Median 18, \(Q_1 = 14\), \(Q_3 = 22\)
2. (b) IQR = 8
3. (c) Fences 2 and 34: no outliers. Box plot: 9, 14, 18, 22, 28.

1. (a) Median 10, \(Q_1 = 8\), \(Q_3 = 13\), IQR 5
2. (b) Fences 0.5 and 20.5; the outlier is 31
3. (c) Whiskers 5 and 14, box 8 to 13, line at 10, a cross at 31

1. (a) Outliers: 4, 71
2. (b) 18 and 50

1. (a) 200
2. (b) 110
3. (c) 55%

1. (a) Frequencies: 12, 28, 34, 18, 8 (total 100)
2. (b) 46.4

1. (a) Equal widths of 30, heights 9, 24, 40, 20, 7
2. (b) 72.6

1. (a) 25 min
2. (b) \(Q_1 = 15\), \(Q_3 = 36\)
3. (c) Box plot: 0, 15, 25, 36, 60

1. (a) 2, 6, 14, 34, 40
2. (b) Median 33, \(Q_1 = 25\), \(Q_3 = 38\)
3. (c) Five numbers: 0, 25, 33, 38, 50
4. (d) The first group has the higher median (33 against 30); the second group has the larger IQR (19 against 13), so it is more spread out.

1 → B, 2 → C, 3 → A

P → B, Q → C, R → A