Question

Fifty cities provided information on vacancy rates (in %) in local apartments in the following frequency distribution.


Vacancy Rate (%) Relative Frequency
0 < x ≤ 3 0.10
3 < x ≤ 6 0.14
6 < x ≤ 9 0.22
9 < x ≤ 12 0.26
12 < x ≤ 15 0.28

a-1. Construct the frequency distribution, the cumulative frequency distribution, and the cumulative relative frequency distribution. (Round "Cumulative Relative Frequency" answers to 2 decimal places.)

Answer 1

To construct the frequency distribution, we will first calculate the frequencies by multiplying the relative frequency by the total number of cities, which is 50.

Vacancy Rate (%) | Relative Frequency | Frequency
0 < x ≤ 3 | 0.10 | 0.10 * 50 = 5
3 < x ≤ 6 | 0.14 | 0.14 * 50 = 7
6 < x ≤ 9 | 0.22 | 0.22 * 50 = 11
9 < x ≤ 12 | 0.26 | 0.26 * 50 = 13
12 < x ≤ 15 | 0.28 | 0.28 * 50 = 14

The frequency distribution is as follows:

Vacancy Rate (%) | Frequency
0 < x ≤ 3 | 5
3 < x ≤ 6 | 7
6 < x ≤ 9 | 11
9 < x ≤ 12 | 13
12 < x ≤ 15 | 14


To construct the cumulative frequency distribution, we will add up the frequencies as we move down the table.

Vacancy Rate (%) | Frequency | Cumulative Frequency
0 < x ≤ 3 | 5 | 5
3 < x ≤ 6 | 7 | 5 + 7 = 12
6 < x ≤ 9 | 11 | 12 + 11 = 23
9 < x ≤ 12 | 13 | 23 + 13 = 36
12 < x ≤ 15 | 14 | 36 + 14 = 50

The cumulative frequency distribution is as follows:

Vacancy Rate (%) | Frequency | Cumulative Frequency
0 < x ≤ 3 | 5 | 5
3 < x ≤ 6 | 7 | 12
6 < x ≤ 9 | 11 | 23
9 < x ≤ 12 | 13 | 36
12 < x ≤ 15 | 14 | 50


To construct the cumulative relative frequency distribution, we will add up the relative frequencies as we move down the table.

Vacancy Rate (%) | Relative Frequency | Cumulative Relative Frequency
0 < x ≤ 3 | 0.10 | 0.10
3 < x ≤ 6 | 0.14 | 0.10 + 0.14 = 0.24
6 < x ≤ 9 | 0.22 | 0.24 + 0.22 = 0.46
9 < x ≤ 12 | 0.26 | 0.46 + 0.26 = 0.72
12 < x ≤ 15 | 0.28 | 0.72 + 0.28 = 1.00

The cumulative relative frequency distribution is as follows:

Vacancy Rate (%) | Cumulative Relative Frequency
0 < x ≤ 3 | 0.10
3 < x ≤ 6 | 0.24
6 < x ≤ 9 | 0.46
9 < x ≤ 12 | 0.72
12 < x ≤ 15 | 1.00

(Rounded to 2 decimal places)