Histograms and cumulative frequency graphs Problem set B Answers

1. (a) Bars of heights 5, 12, 17, 11, 5 (the frequencies), touching, on a horizontal axis from 0 to 15.
2. (b) Frequency densities 1.8, 4.2, 2, 0.5. Bars of width 5, 5, 10, 20.

1. (a) 22
2. (b) 36

1. (a) 4, 15, 34, 46, 50
2. (b) Points (10, 0), (20, 4), (30, 15), (40, 34), (50, 46), (60, 50) joined in order; the graph ends at (60, 50).

1. (a) 27 minutes
2. (b) 13 minutes
3. (c) 45 minutes
4. (d) 26
5. (e) 5%

1. (a) Median 31.5, \(Q_1 = 27.5\), \(Q_3 = 35.5\)
2. (b) IQR = 8
3. (c) Fences 15.5 and 47.5: no outliers. Box plot: 24, 27.5, 31.5, 35.5, 40.

1. (a) Median 44.5, \(Q_1 = 41\), \(Q_3 = 48\), IQR 7
2. (b) Fences 30.5 and 58.5; the outlier is 3
3. (c) Whiskers 38 and 52, box 41 to 48, line at 44.5, a cross at 3

1. (a) Outliers: 82
2. (b) 15 and 57

1. (a) 100
2. (b) 60
3. (c) 60%

1. (a) Frequencies: 6, 15, 24, 10, 5 (total 60)
2. (b) 17.5

1. (a) Equal widths of 10, heights 7, 18, 27, 18, 10
2. (b) 25.8

1. (a) 35 g
2. (b) \(Q_1 = 28\), \(Q_3 = 42\)
3. (c) Box plot: 10, 28, 35, 42, 60

1. (a) 5, 15, 40, 50, 60
2. (b) Median 36, \(Q_1 = 30\), \(Q_3 = 45\)
3. (c) Five numbers: 10, 30, 36, 45, 60
4. (d) The second group has the higher median (41 against 36); the second group has the larger IQR (24 against 15), so it is more spread out.

1 → C, 2 → A, 3 → B

P → C, Q → A, R → B