Quartiles, box plots and outliers Problem set B Answers

48.29

44

1. (a) 29, 34, 41, 47, 52
2. (b) 13

1. (a) 58, 66, 72, 80, 90
2. (b) 13

3.69

mean 41.56, standard deviation 2.31

1. (a) lower fence 4, upper fence 68
2. (b) 3: an outlier; 66: not an outlier; 70: an outlier

outliers: 18, 95

1. (a) mean 42.71, median 27
2. (b) the median: the extreme value pulls the mean up

1. (a) Class P: 8; Class Q: 4
2. (b) Same median (9 minutes); Class P is more spread out (IQR 8 against 4), so Class Q is more consistent

1. (a) 455 g (upper fence 414)
2. (b) any sensible reason, such as: the loaf may have been made with too much dough, or the mass may have been recorded wrongly

outlier 112; whiskers 52 to 70, box 57.5 to 67, median 62, cross at 112

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

1. (a) median 26, IQR 7
2. (b) upper fence 41.5; 55 is above it
3. (c) Batch 2 has the higher median (28 against 26) and the smaller IQR (6 against 7): it is higher and more consistent
4. (d) positive skew (long upper tail); the mean is greater than the median

89