Question
Rowen conducts a survey to record the number of movies bought by each customer during a weeklong sale at his store.
Number of Movies, upper X Frequency
1 25
2 40
3 35
4 45
5 20
6 15
Rowen calculates the relative frequencies and rounds to the nearest whole percent. Which of the following is the correct cumulative relative frequency graph for Rowen’s data?
(1 point)
Responses
A graph is shown.The vertical axis is labeled cumulative relative frequency and ranges from 0 to 50 in increments of 2. A horizontal axis is labeled upper X and ranges from 0 to 6 in increments of 0.1. From left to right the following points are plotted: left parenthesis 1 comma 25 right parenthesis, left parenthesis 2 comma 40 right parenthesis, left parenthesis 3 comma 35 right parenthesis, left parenthesis 4 comma 45 right parenthesis, left parenthesis 5 comma 20 right parenthesis, and left parenthesis 6 comma 15 right parenthesis. Consecutive points are connected by line segments.
Image with alt text: A graph is shown. The vertical axis is labeled cumulative relative frequency and ranges from 0 to 50 in increments of 2. A horizontal axis is labeled upper X and ranges from 0 to 6 in increments of 0.1. From left to right the following points are plotted: left parenthesis 1 comma 25 right parenthesis, left parenthesis 2 comma 40 right parenthesis, left parenthesis 3 comma 35 right parenthesis, left parenthesis 4 comma 45 right parenthesis, left parenthesis 5 comma 20 right parenthesis, and left parenthesis 6 comma 15 right parenthesis. Consecutive points are connected by line segments.
A graph is shown.The vertical axis is labeled cumulative relative frequency and ranges from 0 to 1 in increments of 0.1. A horizontal axis is labeled upper X and ranges from 0 to 6 in increments of 0.1. From left to right the following points are plotted: left parenthesis 1 comma 0.14 right parenthesis, left parenthesis 2 comma 0.22 right parenthesis, left parenthesis 3 comma 0.19 right parenthesis, left parenthesis 4 comma 0.25 right parenthesis, left parenthesis 5 comma 0.11 right parenthesis, and left parenthesis 6 comma 0.08 right parenthesis. Consecutive points are connected by line segments.
Image with alt text: A graph is shown. The vertical axis is labeled cumulative relative frequency and ranges from 0 to 1 in increments of 0.1. A horizontal axis is labeled upper X and ranges from 0 to 6 in increments of 0.1. From left to right the following points are plotted: left parenthesis 1 comma 0.14 right parenthesis, left parenthesis 2 comma 0.22 right parenthesis, left parenthesis 3 comma 0.19 right parenthesis, left parenthesis 4 comma 0.25 right parenthesis, left parenthesis 5 comma 0.11 right parenthesis, and left parenthesis 6 comma 0.08 right parenthesis. Consecutive points are connected by line segments.
A graph is shown.The vertical axis is labeled cumulative relative frequency and ranges from 0 to 200 in increments of 10. A horizontal axis is labeled upper X and ranges from 0 to 6 in increments of 0.11. From left to right the following points are plotted: left parenthesis 1 comma 25 right parenthesis, left parenthesis 2 comma 65 right parenthesis, left parenthesis 3 comma 100 right parenthesis, left parenthesis 4 comma 145 right parenthesis, left parenthesis 5 comma 165 right parenthesis, and left parenthesis 6 comma 180 right parenthesis. Consecutive points are connected by line segments.
Image with alt text: A graph is shown. The vertical axis is labeled cumulative relative frequency and ranges from 0 to 200 in increments of 10. A horizontal axis is labeled upper X and ranges from 0 to 6 in increments of 0.11. From left to right the following points are plotted: left parenthesis 1 comma 25 right parenthesis, left parenthesis 2 comma 65 right parenthesis, left parenthesis 3 comma 100 right parenthesis, left parenthesis 4 comma 145 right parenthesis, left parenthesis 5 comma 165 right parenthesis, and left parenthesis 6 comma 180 right parenthesis. Consecutive points are connected by line segments.
A graph is shown.The vertical axis is labeled cumulative relative frequency and ranges from 0 to 1 in increments of 0.1. A horizontal axis is labeled upper X and ranges from 0 to 6 in increments of 0.1. From left to right the following points are plotted: left parenthesis 1 comma 0.14 right parenthesis, left parenthesis 2 comma 0.36 right parenthesis, left parenthesis 3 comma 0.55 right parenthesis, left parenthesis 4 comma 0.8 right parenthesis, left parenthesis 5 comma 0.91 right parenthesis, and left parenthesis 6 comma 1 right parenthesis. Consecutive points are connected by line segments.
Image with alt text: A graph is shown. The vertical axis is labeled cumulative relative frequency and ranges from 0 to 1 in increments of 0.1. A horizontal axis is labeled upper X and ranges from 0 to 6 in increments of 0.1. From left to right the following points are plotted: left parenthesis 1 comma 0.14 right parenthesis, left parenthesis 2 comma 0.36 right parenthesis, left parenthesis 3 comma 0.55 right parenthesis, left parenthesis 4 comma 0.8 right parenthesis, left parenthesis 5 comma 0.91 right parenthesis, and left parenthesis 6 comma 1 right parenthesis. Consecutive points are connected by line segments.
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Number of Movies, upper X Frequency
1 25
2 40
3 35
4 45
5 20
6 15
Rowen calculates the relative frequencies and rounds to the nearest whole percent. Which of the following is the correct cumulative relative frequency graph for Rowen’s data?
(1 point)
Responses
A graph is shown.The vertical axis is labeled cumulative relative frequency and ranges from 0 to 50 in increments of 2. A horizontal axis is labeled upper X and ranges from 0 to 6 in increments of 0.1. From left to right the following points are plotted: left parenthesis 1 comma 25 right parenthesis, left parenthesis 2 comma 40 right parenthesis, left parenthesis 3 comma 35 right parenthesis, left parenthesis 4 comma 45 right parenthesis, left parenthesis 5 comma 20 right parenthesis, and left parenthesis 6 comma 15 right parenthesis. Consecutive points are connected by line segments.
Image with alt text: A graph is shown. The vertical axis is labeled cumulative relative frequency and ranges from 0 to 50 in increments of 2. A horizontal axis is labeled upper X and ranges from 0 to 6 in increments of 0.1. From left to right the following points are plotted: left parenthesis 1 comma 25 right parenthesis, left parenthesis 2 comma 40 right parenthesis, left parenthesis 3 comma 35 right parenthesis, left parenthesis 4 comma 45 right parenthesis, left parenthesis 5 comma 20 right parenthesis, and left parenthesis 6 comma 15 right parenthesis. Consecutive points are connected by line segments.
A graph is shown.The vertical axis is labeled cumulative relative frequency and ranges from 0 to 1 in increments of 0.1. A horizontal axis is labeled upper X and ranges from 0 to 6 in increments of 0.1. From left to right the following points are plotted: left parenthesis 1 comma 0.14 right parenthesis, left parenthesis 2 comma 0.22 right parenthesis, left parenthesis 3 comma 0.19 right parenthesis, left parenthesis 4 comma 0.25 right parenthesis, left parenthesis 5 comma 0.11 right parenthesis, and left parenthesis 6 comma 0.08 right parenthesis. Consecutive points are connected by line segments.
Image with alt text: A graph is shown. The vertical axis is labeled cumulative relative frequency and ranges from 0 to 1 in increments of 0.1. A horizontal axis is labeled upper X and ranges from 0 to 6 in increments of 0.1. From left to right the following points are plotted: left parenthesis 1 comma 0.14 right parenthesis, left parenthesis 2 comma 0.22 right parenthesis, left parenthesis 3 comma 0.19 right parenthesis, left parenthesis 4 comma 0.25 right parenthesis, left parenthesis 5 comma 0.11 right parenthesis, and left parenthesis 6 comma 0.08 right parenthesis. Consecutive points are connected by line segments.
A graph is shown.The vertical axis is labeled cumulative relative frequency and ranges from 0 to 200 in increments of 10. A horizontal axis is labeled upper X and ranges from 0 to 6 in increments of 0.11. From left to right the following points are plotted: left parenthesis 1 comma 25 right parenthesis, left parenthesis 2 comma 65 right parenthesis, left parenthesis 3 comma 100 right parenthesis, left parenthesis 4 comma 145 right parenthesis, left parenthesis 5 comma 165 right parenthesis, and left parenthesis 6 comma 180 right parenthesis. Consecutive points are connected by line segments.
Image with alt text: A graph is shown. The vertical axis is labeled cumulative relative frequency and ranges from 0 to 200 in increments of 10. A horizontal axis is labeled upper X and ranges from 0 to 6 in increments of 0.11. From left to right the following points are plotted: left parenthesis 1 comma 25 right parenthesis, left parenthesis 2 comma 65 right parenthesis, left parenthesis 3 comma 100 right parenthesis, left parenthesis 4 comma 145 right parenthesis, left parenthesis 5 comma 165 right parenthesis, and left parenthesis 6 comma 180 right parenthesis. Consecutive points are connected by line segments.
A graph is shown.The vertical axis is labeled cumulative relative frequency and ranges from 0 to 1 in increments of 0.1. A horizontal axis is labeled upper X and ranges from 0 to 6 in increments of 0.1. From left to right the following points are plotted: left parenthesis 1 comma 0.14 right parenthesis, left parenthesis 2 comma 0.36 right parenthesis, left parenthesis 3 comma 0.55 right parenthesis, left parenthesis 4 comma 0.8 right parenthesis, left parenthesis 5 comma 0.91 right parenthesis, and left parenthesis 6 comma 1 right parenthesis. Consecutive points are connected by line segments.
Image with alt text: A graph is shown. The vertical axis is labeled cumulative relative frequency and ranges from 0 to 1 in increments of 0.1. A horizontal axis is labeled upper X and ranges from 0 to 6 in increments of 0.1. From left to right the following points are plotted: left parenthesis 1 comma 0.14 right parenthesis, left parenthesis 2 comma 0.36 right parenthesis, left parenthesis 3 comma 0.55 right parenthesis, left parenthesis 4 comma 0.8 right parenthesis, left parenthesis 5 comma 0.91 right parenthesis, and left parenthesis 6 comma 1 right parenthesis. Consecutive points are connected by line segments.
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Answers
GPT-4o mini
To find the cumulative relative frequency graph for Rowen’s data, we first need to perform the following steps:
1. **Calculate the total frequency** of all the customers.
2. **Calculate the relative frequency** for each number of movies bought.
3. **Calculate the cumulative relative frequency**.
### Step 1: Calculate Total Frequency
Add up all the frequencies:
- Total Frequency = 25 (for 1 movie) + 40 (for 2 movies) + 35 (for 3 movies) + 45 (for 4 movies) + 20 (for 5 movies) + 15 (for 6 movies)
- Total Frequency = 25 + 40 + 35 + 45 + 20 + 15 = 170
### Step 2: Calculate Relative Frequency
The relative frequency for each category is obtained by dividing each frequency by the total frequency:
- Relative Frequency for 1 movie = 25 / 170 ≈ 0.147 (rounded to 0.14)
- Relative Frequency for 2 movies = 40 / 170 ≈ 0.235 (rounded to 0.24)
- Relative Frequency for 3 movies = 35 / 170 ≈ 0.206 (rounded to 0.21)
- Relative Frequency for 4 movies = 45 / 170 ≈ 0.265 (rounded to 0.27)
- Relative Frequency for 5 movies = 20 / 170 ≈ 0.118 (rounded to 0.12)
- Relative Frequency for 6 movies = 15 / 170 ≈ 0.088 (rounded to 0.09)
### Step 3: Calculate Cumulative Relative Frequency
Now, we will calculate the cumulative relative frequency:
- Cumulative Relative Frequency for 1 movie: 0.14
- Cumulative Relative Frequency for 2 movies: 0.14 + 0.24 = 0.38
- Cumulative Relative Frequency for 3 movies: 0.38 + 0.21 = 0.59
- Cumulative Relative Frequency for 4 movies: 0.59 + 0.27 = 0.86
- Cumulative Relative Frequency for 5 movies: 0.86 + 0.12 = 0.98
- Cumulative Relative Frequency for 6 movies: 0.98 + 0.09 = 1.00
### Points for the Cumulative Relative Frequency Graph
After calculating the cumulative relative frequencies, we have:
- (1, 0.14)
- (2, 0.38)
- (3, 0.59)
- (4, 0.86)
- (5, 0.98)
- (6, 1)
Looking at the available graphs, we compare the coordinates. The correct graph will have the following points:
1. (1, 0.14)
2. (2, 0.38)
3. (3, 0.59)
4. (4, 0.86)
5. (5, 0.98)
6. (6, 1)
From the options provided, the one that depicts these coordinates and properly represents the cumulative relative frequency is likely to be:
- **The graph that shows points: (1, 0.14), (2, 0.36), (3, 0.55), (4, 0.8), (5, 0.91), and (6, 1)**, assuming that the values are appropriately rounded and represent cumulative relative frequencies correctly.
Review these points against the provided options to select the correct graph.
1. **Calculate the total frequency** of all the customers.
2. **Calculate the relative frequency** for each number of movies bought.
3. **Calculate the cumulative relative frequency**.
### Step 1: Calculate Total Frequency
Add up all the frequencies:
- Total Frequency = 25 (for 1 movie) + 40 (for 2 movies) + 35 (for 3 movies) + 45 (for 4 movies) + 20 (for 5 movies) + 15 (for 6 movies)
- Total Frequency = 25 + 40 + 35 + 45 + 20 + 15 = 170
### Step 2: Calculate Relative Frequency
The relative frequency for each category is obtained by dividing each frequency by the total frequency:
- Relative Frequency for 1 movie = 25 / 170 ≈ 0.147 (rounded to 0.14)
- Relative Frequency for 2 movies = 40 / 170 ≈ 0.235 (rounded to 0.24)
- Relative Frequency for 3 movies = 35 / 170 ≈ 0.206 (rounded to 0.21)
- Relative Frequency for 4 movies = 45 / 170 ≈ 0.265 (rounded to 0.27)
- Relative Frequency for 5 movies = 20 / 170 ≈ 0.118 (rounded to 0.12)
- Relative Frequency for 6 movies = 15 / 170 ≈ 0.088 (rounded to 0.09)
### Step 3: Calculate Cumulative Relative Frequency
Now, we will calculate the cumulative relative frequency:
- Cumulative Relative Frequency for 1 movie: 0.14
- Cumulative Relative Frequency for 2 movies: 0.14 + 0.24 = 0.38
- Cumulative Relative Frequency for 3 movies: 0.38 + 0.21 = 0.59
- Cumulative Relative Frequency for 4 movies: 0.59 + 0.27 = 0.86
- Cumulative Relative Frequency for 5 movies: 0.86 + 0.12 = 0.98
- Cumulative Relative Frequency for 6 movies: 0.98 + 0.09 = 1.00
### Points for the Cumulative Relative Frequency Graph
After calculating the cumulative relative frequencies, we have:
- (1, 0.14)
- (2, 0.38)
- (3, 0.59)
- (4, 0.86)
- (5, 0.98)
- (6, 1)
Looking at the available graphs, we compare the coordinates. The correct graph will have the following points:
1. (1, 0.14)
2. (2, 0.38)
3. (3, 0.59)
4. (4, 0.86)
5. (5, 0.98)
6. (6, 1)
From the options provided, the one that depicts these coordinates and properly represents the cumulative relative frequency is likely to be:
- **The graph that shows points: (1, 0.14), (2, 0.36), (3, 0.55), (4, 0.8), (5, 0.91), and (6, 1)**, assuming that the values are appropriately rounded and represent cumulative relative frequencies correctly.
Review these points against the provided options to select the correct graph.