Question
Fifty cities provided information on vacancy rates (in %) in local apartments in the following frequency distribution.
Vacancy Rate (%) Relative Frequency
0 < x ≤ 3 0.14
3 < x ≤ 6 0.20
6 < x ≤ 9 0.36
9 < x ≤ 12 0.20
12 < x ≤ 15 0.10
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.)
a-2. How many of the cities had a vacancy rate of more than 6% but no more than 9%?
a-3. How many of the cities had a vacancy rate of 9% or less?
a-4. What proportion of the cities had a vacancy rate of more than 9%? (Round your answer to 2 decimal places.)
b. Which statement is correct regarding the shape of the distribution using a histogram?
multiple choice
The distribution is relatively symmetric.
The distribution is positively skewed.
The distribution is negatively skewed.
Symmetry or skewness cannot be determined with the available information..
Vacancy Rate (%) Relative Frequency
0 < x ≤ 3 0.14
3 < x ≤ 6 0.20
6 < x ≤ 9 0.36
9 < x ≤ 12 0.20
12 < x ≤ 15 0.10
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.)
a-2. How many of the cities had a vacancy rate of more than 6% but no more than 9%?
a-3. How many of the cities had a vacancy rate of 9% or less?
a-4. What proportion of the cities had a vacancy rate of more than 9%? (Round your answer to 2 decimal places.)
b. Which statement is correct regarding the shape of the distribution using a histogram?
multiple choice
The distribution is relatively symmetric.
The distribution is positively skewed.
The distribution is negatively skewed.
Symmetry or skewness cannot be determined with the available information..
Answers
There are no human answers yet.
Answered by
GPT 3.5
a-1. To construct the frequency distribution, we can use the given relative frequencies to calculate the frequencies for each category:
Vacancy Rate (%) Relative Frequency Frequency
0 < x ≤ 3 0.14 (0.14)(50) = 7
3 < x ≤ 6 0.20 (0.20)(50) = 10
6 < x ≤ 9 0.36 (0.36)(50) = 18
9 < x ≤ 12 0.20 (0.20)(50) = 10
12 < x ≤ 15 0.10 (0.10)(50) = 5
The frequency distribution is as follows:
Vacancy Rate (%) Frequency
0 < x ≤ 3 7
3 < x ≤ 6 10
6 < x ≤ 9 18
9 < x ≤ 12 10
12 < x ≤ 15 5
To construct the cumulative frequency distribution, we simply add up the frequencies from the frequency distribution:
Vacancy Rate (%) Frequency Cumulative Frequency
0 < x ≤ 3 7 7
3 < x ≤ 6 10 17
6 < x ≤ 9 18 35
9 < x ≤ 12 10 45
12 < x ≤ 15 5 50
To construct the cumulative relative frequency distribution, we add up the relative frequencies:
Vacancy Rate (%) Relative Frequency Cumulative Relative Freq.
0 < x ≤ 3 0.14 0.14
3 < x ≤ 6 0.20 0.34
6 < x ≤ 9 0.36 0.70
9 < x ≤ 12 0.20 0.90
12 < x ≤ 15 0.10 1.00
a-2. To find the number of cities with a vacancy rate of more than 6% but no more than 9%, we subtract the cumulative frequency for 6 < x ≤ 9 from the cumulative frequency for 3 < x ≤ 6. In this case, it is 18 - 10 = 8 cities.
a-3. To find the number of cities with a vacancy rate of 9% or less, we can use the cumulative frequency for 9 < x ≤ 12, which is 45 cities.
a-4. To find the proportion of cities with a vacancy rate of more than 9%, we can subtract the cumulative relative frequency for 9 < x ≤ 12 from 1: 1 - 0.9 = 0.1. So, 10% of the cities had a vacancy rate of more than 9%.
b. Symmetry or skewness cannot be determined with the available information.
Vacancy Rate (%) Relative Frequency Frequency
0 < x ≤ 3 0.14 (0.14)(50) = 7
3 < x ≤ 6 0.20 (0.20)(50) = 10
6 < x ≤ 9 0.36 (0.36)(50) = 18
9 < x ≤ 12 0.20 (0.20)(50) = 10
12 < x ≤ 15 0.10 (0.10)(50) = 5
The frequency distribution is as follows:
Vacancy Rate (%) Frequency
0 < x ≤ 3 7
3 < x ≤ 6 10
6 < x ≤ 9 18
9 < x ≤ 12 10
12 < x ≤ 15 5
To construct the cumulative frequency distribution, we simply add up the frequencies from the frequency distribution:
Vacancy Rate (%) Frequency Cumulative Frequency
0 < x ≤ 3 7 7
3 < x ≤ 6 10 17
6 < x ≤ 9 18 35
9 < x ≤ 12 10 45
12 < x ≤ 15 5 50
To construct the cumulative relative frequency distribution, we add up the relative frequencies:
Vacancy Rate (%) Relative Frequency Cumulative Relative Freq.
0 < x ≤ 3 0.14 0.14
3 < x ≤ 6 0.20 0.34
6 < x ≤ 9 0.36 0.70
9 < x ≤ 12 0.20 0.90
12 < x ≤ 15 0.10 1.00
a-2. To find the number of cities with a vacancy rate of more than 6% but no more than 9%, we subtract the cumulative frequency for 6 < x ≤ 9 from the cumulative frequency for 3 < x ≤ 6. In this case, it is 18 - 10 = 8 cities.
a-3. To find the number of cities with a vacancy rate of 9% or less, we can use the cumulative frequency for 9 < x ≤ 12, which is 45 cities.
a-4. To find the proportion of cities with a vacancy rate of more than 9%, we can subtract the cumulative relative frequency for 9 < x ≤ 12 from 1: 1 - 0.9 = 0.1. So, 10% of the cities had a vacancy rate of more than 9%.
b. Symmetry or skewness cannot be determined with the available information.
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.