1. Fifty cities provided information on vacancy rates (in percent) in local apartments in the following frequency distribution. Vacancy Rate (in percent) Frequency 0 up to 3 5 3 up to 6 10 6 up to 9 20 9 up to 12 10 12 up to 15 5 a. Construct the relative frequency distribution, the cumulative frequency distribution, and the cumulative relative frequency distribution. b. How many of the cities had a vacancy rate less than 12%? What percent of the cities had a vacancy rate of at least 6% but less than 9%? What percent of the cities had a vacancy rate of less than 9%? c. Graph the frequency histogram. Comment on the shape of the distribution.
1. Fifty cities provided information on vacancy rates (in percent) in local apartments in the following frequency distribution.
|
Vacancy Rate (in percent) |
Frequency |
|
0 up to 3 |
5 |
|
3 up to 6 |
10 |
|
6 up to 9 |
20 |
|
9 up to 12 |
10 |
|
12 up to 15 |
5 |
a. Construct the relative frequency distribution, the cumulative frequency distribution, and the cumulative relative frequency distribution.
b. How many of the cities had a vacancy rate less than 12%? What percent of the cities had a vacancy rate of at least 6% but less than 9%? What percent of the cities had a vacancy rate of less than 9%?
c. Graph the frequency histogram. Comment on the shape of the distribution.
- The following frequency table is given to us.
|
Vacancy Rate (in percent) |
Frequency |
|
0 up to 3 |
5 |
|
3 up to 6 |
10 |
|
6 up to 9 |
20 |
|
9 up to 12 |
10 |
|
12 up to 15 |
5 |
We have to construct
- the relative frequency distribution
- the cumulative frequency distribution
- the cumulative relative frequency distribution.
- The relative frequency distribution.
The formula for relative frequency is as follows.
Thus, the relative frequency distribution would be as follows.
|
Vacancy Rate (in percent) |
Frequency |
Relative Frequency |
|
0 up to 3 |
5 |
0.1 |
|
3 up to 6 |
10 |
0.2 |
|
6 up to 9 |
20 |
0.4 |
|
9 up to 12 |
10 |
0.2 |
|
12 up to 15 |
5 |
0.1 |
|
Total → |
50 |
1 |
- The cumulative frequency distribution
The cumulative frequency is calculated by adding each frequency from a frequency distribution table to the sum of its predecessors.
The last value will always be equal to the total for all observations since all frequencies will already have been added to the previous total.
Thus, the relative frequency distribution would be as follows.
|
Vacancy Rate (in percent) |
Frequency |
Cumulative Frequency |
|
0 up to 3 |
5 |
5 |
|
3 up to 6 |
10 |
15 |
|
6 up to 9 |
20 |
35 |
|
9 up to 12 |
10 |
45 |
|
12 up to 15 |
5 |
50 |
|
Total → |
50 |
- |
- The cumulative relative frequency distribution.
The cumulative relative frequency is calculated by adding each relative frequency from a relative frequency distribution table to the sum of its predecessors.
|
Vacancy Rate (in percent) |
Frequency |
Relative Frequency |
cumulative relative frequency |
|
0 up to 3 |
5 |
0.1 |
0.1 |
|
3 up to 6 |
10 |
0.2 |
0.3 |
|
6 up to 9 |
20 |
0.4 |
0.7 |
|
9 up to 12 |
10 |
0.2 |
0.9 |
|
12 up to 15 |
5 |
0.1 |
1 |
|
Total → |
50 |
1 |
- |
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