(a) Plot the histogram and frequency polygon for each year on separate
graphs.
(b)Plot the two cumulative frequency graphs in one figure.
(c) Find and compare the medians.2.3 A study on the e¤ects of exercise on the menstrual cycle provides the
following ages (years) of menarche (the beginning of menstruation) for
96 female swimmers who began training prior to menarche.
15.0 17.1 14.6 15.2 14.9 14.4 14.7 15.3
13.6 15.1 16.2 15.9 13.8 15.0 15.4 14.9
14.2 16.5 13.2 16.8 15.3 14.7 13.9 16.1
15.4 14.6 15.2 14.8 13.7 16.3 15.1 14.5
16.4 13.6 14.8 15.5 13.9 15.9 16.0 14.6
14.0 15.1 14.8 15.0 14.8 15.3 15.7 14.3
13.9 15.6 15.4 14.6 15.2 14.8 13.7 16.3
15.1 14.5 13.6 15.1 16.2 15.9 13.8 15.0
15.4 14.9 16.2 15.9 13.8 15.0 15.4 14.9
14.2 16.5 13.4 16.5 14.8 15.1 14.9 13.7
16.2 15.8 15.4 14.7 14.3 15.2 14.6 13.7
14.9 15.8 15.1 14.6 13.8 16.0 15.0 14.6(a) Form a frequency distribution including relative frequencies and
cumulative relative frequencies.
(b)Plot the frequency polygon and cumulative frequency graph.
(c) Find the median and 95th percentile.2.4 The following are the menarchal ages (in years) of 56 female swimmers
who began training after they had reached menarche.
14.0 16.1 13.4 14.6 13.7 13.2 13.7 14.3
12.9 14.1 15.1 14.8 12.8 14.2 14.1 13.6
14.2 15.8 12.7 15.6 14.1 13.0 12.9 15.1
15.0 13.6 14.2 13.8 12.7 15.3 14.1 13.5
15.3 12.6 13.8 14.4 12.9 14.6 15.0 13.8
13.0 14.1 13.8 14.2 13.6 14.1 14.5 13.1
12.8 14.3 14.2 13.5 14.1 13.6 12.4 15.1(a) Form a frequency distribution using the same age intervals as in
Exercise 2.3. (These intervals may be di¤erent from those in Exam-
ple 2.3.)
(b)Display on the same graph two cumulative frequency graphs, one
for the group trained before menarche and one for the group trained
after menarche. Compare these two graphs and draw your conclu-
sion.EXERCISES 93