Relative Frequency
Once we have an understanding of frequency tables and histograms, the relative
frequency table and relative frequency histogram are very easy to construct. To find
relative frequency we use he following formula:
Relative Frequency = f =
class frequency
n total of all frequencies
We can put this as one of our columns in our relative frequency table.
For example: In a health care utilization study, a random sample of 25 patients having
total care insurance at a designated clinic was studied. The number of times each patient
went to the clinic during a one-year period was recorded. The results follow:
15
7
3
13
1
22
12
4
3
8
12
15
11
19
3
2
5
3
4
7
2
13
6
5
4
A) Construct a relative frequency table using five classes.
B) Construct a relative frequency histogram using the same classes.
Solution:
Since we already have an understanding of the frequency table, we should
know how to come up with the 5 classes.
Health Care Utilization Study of 25 Patients
Class Boundary
Tally
Frequency
.5 – 5.5
5.5 – 10.5
10.5 – 15.5
15.5 – 20.5
20.5 – 25.5
Total =
Relative Frequency
Under the frequency column, there is a total. We will take the individual frequency for
each class and divide it by the total frequency, which in this case will be 25. For the first
class, we tally equals 12. We now take 12 and divide it by 25 to get .48.
***Hint: If take a total of the relative frequency column, you should always get
approximately 1.
Now, we will construct the relative frequency histogram. The horizontal column would
remain the same as if we were constructing a regular histogram. The vertical axis will be
marked with relative frequencies instead of the actual frequencies.
Examples:
1) Home Video Incorporated rents out new releases. A random sample of 32
days gave the following information about the number of new releases rented
each day at one of he local stores:
12
27
29
4
21
38
21
5
15
25
23
10
8
22
13
17
43
8
22
23
26
28
31
35
26
34
36
33
32
39
37
29
A) Construct a relative frequency table using 5 classes.
B) Construct a relative frequency histogram.
2) The district manager of a suburban park and recreation area wants to estimate
the amount of time people spend in their local park in July. A random sample
of 50 local residents gave the following information on the estimated number
of hours they spent in the regional park during the month of July:
8
5
9
12
15
18
2
3
5
4
2
8
6
10
13
14
8
10
9
13
21
2
4
3
7
7
6
7
6
16
19
11
3
3
8
4
11
10
9
8
6
6
6
7
8
12
6
7
20
7
A) Construct a relative frequency table using 7 classes.
B) Construct a relative frequency histogram.
3) The American Association of Registered Dentists wants to estimate the
number of fillings an adult (over 18 years of age) has accumulated. A random
sample of 36 dental records gave the following information:
8
9
19
5
13
14
5
6
12
13
3
6
5
11
6
7
4
11
23
5
32
25
21
6
7
11
12
8
15
16
17
9
10
8
22
18
A) Construct a relative frequency table using 6 classes.
B) Construct a relative frequency histogram.
4) A random sample 0f 42 auto insurance claims made on Any State Insurance
Company gave the following information rounded to the nearest dollar:
705
800
1090 2408 2010 910
350
690
520
750
1000 860
170
1100
1150 1590 1841 1880 1942 2210 1886
1954 1710 1372 1200 1210 1351 1400
1790 1682 1310 1460 1550 1300 1463
1511 1190 1200 510
1285 1700 2350
A) Construct a relative frequency table using 8 classes.
B) Construct a relative frequency histogram.
5) Nurses on the eight floor of Community Hospital believe they need extra
staffing at night. To estimate the night workload, a random sample of 35 nights
was used. For each night the total number of room calls to the nurses’ station on
the eighth floor was recorded:
68
70
86
18
90
100
101
95
80
70
73
82
71
37
102
87
46
58
62
63
92
70
69
85
84
86
90
77
60
74
83
86
75
71
88
A) Construct a relative frequency table using 5 classes.
B) Construct a relative frequency histogram.