Example 2.3 A study was conducted to investigate the possible e¤ects of
exercise on the menstrual cycle. From the data collected from that study, we
obtained the menarchal age (in years) of 56 female swimmers who began their
swimming training after they had reached menarche; these served as controls to
compare with those who began their training prior to 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 15.1From this data set we have the following:
- The smallest number is 12.4 and the largest is 16.1, so that
R¼ 16 : 1 12 : 4
¼ 3 : 7If five intervals are used, we would havew¼3 : 7
5
¼ 0 : 74
and if 15 intervals are used, we would havew¼3 : 7
15
¼ 0 : 25
TABLE 2.2
Weight
Interval (lb) Tally Frequency
Relative
Frequency (%)10–19 kk 5 8.8
20–29 kkkkkkkk 19 33.3
30–39 kkkk 10 17.5
40–49 kkkkjjj 13 22.8
50–59 jjjj 4 7.0
60–69 jjjj 4 7.0
70–79 jj 2 3.5
Total 57 100.0
TABULAR AND GRAPHICAL METHODS 61