Question

2.3.1 In a study of the oral home care practice and reasons for seeking dental care among individuals
on renal dialysis, Atassi (A-1) studied 90 subjects on renal dialysis. The oral hygiene status of all
subjects was examined using a plaque index with a range of 0 to 3 10 = no soft plaque deposits,
+
+
FIGURE 2.3.8 Stem-and-leaf display prepared by MINITAB from the data on subjects’
ages shown in Table 2.2.1; class interval width " 5.
Stem-and-leaf of Age N = 189
Leaf Unit = 1.0
2 3 04
11 3 577888899
28 4 00223333334444444
57 4 55566666677777788888889999999
(46) 5 0000000011112222223333333333333333344444444444
86 5 555666666777777788999999
62 6 000011111111111222222233444444
32 6 556666667888999
17 7 0111111123
7 7 567888
1 8 2
EXERCISES 31
abundance of soft plaque deposits). The following table shows the plaque index scores for
all 90 subjects.
1.17 2.50 2.00 2.33 1.67 1.33
1.17 2.17 2.17 1.33 2.17 2.00
2.17 1.17 2.50 2.00 1.50 1.50
1.00 2.17 2.17 1.67 2.00 2.00
1.33 2.17 2.83 1.50 2.50 2.33
0.33 2.17 1.83 2.00 2.17 2.00
1.00 2.17 2.17 1.33 2.17 2.50
0.83 1.17 2.17 2.50 2.00 2.50
0.50 1.50 2.00 2.00 2.00 2.00
1.17 1.33 1.67 2.17 1.50 2.00
1.67 0.33 1.50 2.17 2.33 2.33
1.17 0.00 1.50 2.33 1.83 2.67
0.83 1.17 1.50 2.17 2.67 1.50
2.00 2.17 1.33 2.00 2.33 2.00
2.17 2.17 2.00 2.17 2.00 2.17
Source: Farhad Atassi, DDS, MSc, FICOI.
Used with permission.
(a) Use these data to prepare:
A frequency distribution
A relative frequency distribution
A cumulative frequency distribution
A cumulative relative frequency distribution
A histogram
A frequency polygon
(b) What percentage of the measurements are less than 2.00?
(c) What proportion of the subjects have measurements greater than or equal to 1.50?
(d) What percentage of the measurements are between 1.50 and 1.99 inclusive?
(e) How many of the measurements are greater than 2.49?
(f) What proportion of the measurements are either less than 1.0 or greater than 2.49?
(g) Someone picks a measurement at random from this data set and asks you to guess the value.
What would be your answer? Why?
(h) Frequency distributions and their histograms may be described in a number of ways depending
on their shape. For example, they may be symmetric (the left half is at least approximately a
mirror image of the right half ), skewed to the left (the frequencies tend to increase as the measurements
increase in size), skewed to the right (the frequencies tend to decrease as the measurements
increase in size), or U-shaped (the frequencies are high at each end of the distribution and
small in the center). How would you describe the present distribution?

Answer 1

(b.)

bin label	counts	cumulative
<=0	1	1
0.01-0.49	2	3
0.50-0.99	3	6
1.00-1.49	15	21
1.50-1.99	15	36
2.00-2.49	45	81
>=2.50	9	90

percentage of the measurements are less than 2.00 = 36*100/90= 40 %

(c.) proportion of the subjects have measurements greater than or equal to 1.50 = (15+45+9) / 90 = 0.77

(d.)  percentage of the measurements are between 1.50 and 1.99 inclusive = 15*100/90 = 16.67 %

(e.) measurements are greater than 2.49 = 9

(f.) proportion of the measurements are either less than 1.0 or greater than 2.49 = (1+2+3+9)/90 = 1/6