Quartiles, box plots and outliers Problem set A Answers

31.14

25

1. (a) 8, 11, 17, 22, 28
2. (b) 11

1. (a) 5, 12, 19.5, 27, 36
2. (b) 14

3.85

mean 29.00, standard deviation 2.89

1. (a) lower fence 25, upper fence 97
2. (b) 20: an outlier; 94: not an outlier; 99: an outlier

outliers: 9, 52

1. (a) mean 301.43, median 225
2. (b) the median: the extreme value pulls the mean up

1. (a) Phone X: 5; Phone Y: 2
2. (b) Same median (12 hours); Phone X is more spread out (IQR 5 against 2), so Phone Y is more consistent

1. (a) 15.9 s (upper fence 13.2)
2. (b) any sensible reason, such as: the athlete may have been injured or slipped at the start, or the time may have been recorded wrongly

outlier 64; whiskers 14 to 33, box 19.5 to 30, median 24.5, cross at 64

1. (a) 1
2. (b) Q1 = 0, Q3 = 2, IQR = 2
3. (c) Upper fence 2 + 1.5 × 2 = 5, and 6 > 5

1. (a) median 10, IQR 7
2. (b) upper fence 25.5; 38 is above it
3. (c) Desk 2 has the higher median (12 against 10) and the smaller IQR (5 against 7): it is higher and more consistent
4. (d) positive skew (long upper tail); the mean is greater than the median

48