Question

Hoekema et al. (A-3) studied craniofacial morphology of patients diagnosed with obstructive sleep apnea syndrome (OSAS) in healthy male subjects. One of the demographic variables the researchers collected for all subjects was the Body Mass Index (BMI, calculated by dividingweight in kg by the square of the patients’ height in cm). The following are the BMI values of 29OSAS subjects.

33.57 27.78 33.34 29.01 26.86 54.33 24.21 31.49 34.42

41.50 24.54 41.75 24.49 43.23 29.07 28.21 21.54 27.74

31.44 30.08 40.81 47.78 28.99 27.38 29.39 42.68 47.09 41.10 33.48

A frequency distribution
A relative frequency distribution
A cumulative frequency distribution
A cumulative relative frequency distributions
A histogram and a box-and-whisker plot (use MATLAB, show codes)

A frequency polygon
A stem-and-leaf display for the data. (use MATLAB, show codes)

(b) What percentage of the measurements are less than 30?
(c) What percentage of the measurements are between 30.0 and 49.99 inclusive?
(d) What percentage of the measurements are greater than 34.99?
(e) How many of the measurements are greater than 40?
(f) Describe these data with respect to symmetry/skewness and kurtosis.
(g) Find the mean, median, variance, standard deviation and coefficient of variation of the BMI data.

Answer 1

Frequency distribution:
CI	F
20 - 25	4
25 - 30	9
30 - 35	7
35 - 40	0
40 - 45	6
45 - 50	2
50 - 55	1

Relative frequency distribution
CI	F	Relative F
20 - 25	4	0.138
25 - 30	9	0.310
30 - 35	7	0.241
35 - 40	0	0.000
40 - 45	6	0.207
45 - 50	2	0.069
50 - 55	1	0.034
sum =	29

Cumulative frequency distribution
CI	F	Cumulative F
20 - 25	4	4
25 - 30	9	13
30 - 35	7	20
35 - 40	0	20
40 - 45	6	26
45 - 50	2	28
50 - 55	1	29
sum =	29

Cumulative relative frequency distribution
CI	F	Relative F	Cumulative relative F
20 - 25	4	0.138	0.138
25 - 30	9	0.310	0.448
30 - 35	7	0.241	0.690
35 - 40	0	0.000	0.690
40 - 45	6	0.207	0.897
45 - 50	2	0.069	0.966
50 - 55	1	0.034	1.000
sum =	29