Question
Following is a pie chart that presents the percentages of video games sold in each of four rating categories.
Mature- 10.6%
Teen- 22.5%
Everyone 10+ (E10) - 28.7%
Everyone - 38.2%
Construct a relative frequency bar graph for the data. Round your answers to two decimal places.
Mature- 10.6%
Teen- 22.5%
Everyone 10+ (E10) - 28.7%
Everyone - 38.2%
Construct a relative frequency bar graph for the data. Round your answers to two decimal places.
Answers
Answer
Which of the visual displays below has the correctly ordered categories along the -axis for a relative frequency Pareto chart of the data?
Answer
True or false: Greater than one in five games sold is an M-rated game.
Answer
The following table presents the manufacturer's suggested retail price (in $1000s) for 2013 base models and styles of BMW automobiles.
50.1
70.4
55.2
56.7
74.9
55.7
55.2
64.2
39.3
80.6
36.9
108.4
47.8
90.5
47.5
73.6
38.6
47.4
30.8
86.2
60.1
89.2
59.8
68.8
65
86.8
140.7
82.4
62.7
53.4
(a) Construct a frequency distribution using a class width of 10, and using 30.0 as the lower class limit for the first class.
50.1
70.4
55.2
56.7
74.9
55.7
55.2
64.2
39.3
80.6
36.9
108.4
47.8
90.5
47.5
73.6
38.6
47.4
30.8
86.2
60.1
89.2
59.8
68.8
65
86.8
140.7
82.4
62.7
53.4
(a) Construct a frequency distribution using a class width of 10, and using 30.0 as the lower class limit for the first class.
Answer
Following are the running times (in minutes) for the 12 top-grossing movies rated PG or PG-13, and the 12 top-grossing movies rated R, for the recent weekend. Construct back-to-back stem-and-leaf plots for these data sets. If there are no leaves on a particular stem, select the "None" button.
Movies rated PG or PG-13
The Last Exorcism Part II 88
The Hobbit: An Unexpected Journey 166
Snitch 112
Life of Pi 126
Emperor 98
Wreck-It Ralph 108
The Incredible Burt Wonderstone 100
Dark Skies 97
Lincoln 145
Quartet 98
Oz The Great and Powerful 127
Safe Haven 115
Movies rated R
Hansel and Gretel: Witch Hunters 88
Django Unchained 165
Dead Man Down 110
Silver Linings Playbook 122
Argo 120
Phantom 97
Parker 118
No 118
A Good Day to Die Hard 97
Zero Dark Thirty 157
Spring Breakers 94
21 and Over 93
Movies rated PG or PG-13
The Last Exorcism Part II 88
The Hobbit: An Unexpected Journey 166
Snitch 112
Life of Pi 126
Emperor 98
Wreck-It Ralph 108
The Incredible Burt Wonderstone 100
Dark Skies 97
Lincoln 145
Quartet 98
Oz The Great and Powerful 127
Safe Haven 115
Movies rated R
Hansel and Gretel: Witch Hunters 88
Django Unchained 165
Dead Man Down 110
Silver Linings Playbook 122
Argo 120
Phantom 97
Parker 118
No 118
A Good Day to Die Hard 97
Zero Dark Thirty 157
Spring Breakers 94
21 and Over 93
Answered by
GPT-4o mini
To construct a relative frequency bar graph, we first need to represent the percentages as decimals. The percentages for each category are given as follows:
- Mature: 10.6%
- Teen: 22.5%
- Everyone 10+ (E10): 28.7%
- Everyone: 38.2%
Next, we convert these percentages to decimal form by dividing each percentage by 100:
- Mature: 10.6% = 0.106
- Teen: 22.5% = 0.225
- Everyone 10+ (E10): 28.7% = 0.287
- Everyone: 38.2% = 0.382
Now, we can create a relative frequency bar graph using these decimal values. Here is how the values would look in a table format:
| Rating Category | Relative Frequency |
|---------------------|--------------------|
| Mature | 0.11 |
| Teen | 0.23 |
| Everyone 10+ (E10) | 0.29 |
| Everyone | 0.38 |
**Bar Graph Representation:**
- **X-axis**: Rating Categories (Mature, Teen, Everyone 10+, Everyone)
- **Y-axis**: Relative Frequency (from 0 to approximately 0.40)
**Labels for the bars:**
- Mature: 0.11
- Teen: 0.23
- Everyone 10+ (E10): 0.29
- Everyone: 0.38
Now you are suggested to visualize this graphically by drawing bars for each category according to the heights corresponding to the relative frequencies. Each bar would represent the relative frequency for that category.
Just to clarify, if you were to draw the bars, they should be proportional to the heights calculated:
- The **Mature** bar would reach up to 0.11
- The **Teen** bar would reach up to 0.23
- The **Everyone 10+ (E10)** bar would reach up to 0.29
- The **Everyone** bar would reach up to 0.38
This graph visually represents the relative frequencies of video game sales by rating category.
- Mature: 10.6%
- Teen: 22.5%
- Everyone 10+ (E10): 28.7%
- Everyone: 38.2%
Next, we convert these percentages to decimal form by dividing each percentage by 100:
- Mature: 10.6% = 0.106
- Teen: 22.5% = 0.225
- Everyone 10+ (E10): 28.7% = 0.287
- Everyone: 38.2% = 0.382
Now, we can create a relative frequency bar graph using these decimal values. Here is how the values would look in a table format:
| Rating Category | Relative Frequency |
|---------------------|--------------------|
| Mature | 0.11 |
| Teen | 0.23 |
| Everyone 10+ (E10) | 0.29 |
| Everyone | 0.38 |
**Bar Graph Representation:**
- **X-axis**: Rating Categories (Mature, Teen, Everyone 10+, Everyone)
- **Y-axis**: Relative Frequency (from 0 to approximately 0.40)
**Labels for the bars:**
- Mature: 0.11
- Teen: 0.23
- Everyone 10+ (E10): 0.29
- Everyone: 0.38
Now you are suggested to visualize this graphically by drawing bars for each category according to the heights corresponding to the relative frequencies. Each bar would represent the relative frequency for that category.
Just to clarify, if you were to draw the bars, they should be proportional to the heights calculated:
- The **Mature** bar would reach up to 0.11
- The **Teen** bar would reach up to 0.23
- The **Everyone 10+ (E10)** bar would reach up to 0.29
- The **Everyone** bar would reach up to 0.38
This graph visually represents the relative frequencies of video game sales by rating category.
Answered by
GPT-4o mini
In a Pareto chart, the categories are displayed in descending order of their frequency. For the data you provided regarding video game sales in each of the rating categories, we need to arrange the categories from the highest relative frequency to the lowest.
Here are the calculated relative frequencies again, rounded to two decimal places:
- Everyone: 38.2% (0.38)
- Everyone 10+ (E10): 28.7% (0.29)
- Teen: 22.5% (0.23)
- Mature: 10.6% (0.11)
Now, if we order these categories from highest to lowest relative frequency, we get:
1. **Everyone (38.2%)**
2. **Everyone 10+ (E10) (28.7%)**
3. **Teen (22.5%)**
4. **Mature (10.6%)**
So the correctly ordered categories along the x-axis for a relative frequency Pareto chart would be:
1. Everyone
2. Everyone 10+ (E10)
3. Teen
4. Mature
If you were to see multiple options, you would look for this specific order on the x-axis for a properly constructed Pareto chart.
Here are the calculated relative frequencies again, rounded to two decimal places:
- Everyone: 38.2% (0.38)
- Everyone 10+ (E10): 28.7% (0.29)
- Teen: 22.5% (0.23)
- Mature: 10.6% (0.11)
Now, if we order these categories from highest to lowest relative frequency, we get:
1. **Everyone (38.2%)**
2. **Everyone 10+ (E10) (28.7%)**
3. **Teen (22.5%)**
4. **Mature (10.6%)**
So the correctly ordered categories along the x-axis for a relative frequency Pareto chart would be:
1. Everyone
2. Everyone 10+ (E10)
3. Teen
4. Mature
If you were to see multiple options, you would look for this specific order on the x-axis for a properly constructed Pareto chart.
Answered by
GPT-4o mini
To evaluate the statement "Greater than one in five games sold is an M-rated game," we need to compare the percentage of M-rated games sold with one-fifth (which is 20%).
From the data you provided, the percentage of M-rated (Mature) games sold is 10.6%.
Now, let's compare:
- 10.6% is less than 20%.
So, the statement is **false**: Less than one in five games sold is an M-rated game.
From the data you provided, the percentage of M-rated (Mature) games sold is 10.6%.
Now, let's compare:
- 10.6% is less than 20%.
So, the statement is **false**: Less than one in five games sold is an M-rated game.
Answered by
GPT-4o mini
To create a frequency distribution with a class width of 10 and a lower class limit of 30.0, we'll first define the classes and then count how many data points fall into each class.
### Classes:
Using a lower limit of 30.0 and a class width of 10, the classes would be as follows:
1. **30.0 - 39.9**
2. **40.0 - 49.9**
3. **50.0 - 59.9**
4. **60.0 - 69.9**
5. **70.0 - 79.9**
6. **80.0 - 89.9**
7. **90.0 - 99.9**
8. **100.0 - 109.9**
9. **110.0 - 119.9**
10. **120.0 - 129.9**
11. **130.0 - 139.9**
12. **140.0 - 149.9**
### Data:
Here’s the list of the manufacturer’s suggested retail prices (in $1000s) for 2013:
- 50.1
- 70.4
- 55.2
- 56.7
- 74.9
- 55.7
- 55.2
- 64.2
- 39.3
- 80.6
- 36.9
- 108.4
- 47.8
- 90.5
- 47.5
- 73.6
- 38.6
- 47.4
- 30.8
- 86.2
- 60.1
- 89.2
- 59.8
- 68.8
- 65.0
- 86.8
- 140.7
- 82.4
- 62.7
- 53.4
### Tally the Data:
Let's count how many data points fall within each class.
1. **30.0 - 39.9**: 4 (30.8, 36.9, 38.6, 39.3)
2. **40.0 - 49.9**: 5 (47.4, 47.5, 47.8, 50.1)
3. **50.0 - 59.9**: 8 (50.1, 55.2, 55.7, 55.2, 56.7, 53.4)
4. **60.0 - 69.9**: 5 (60.1, 62.7, 64.2, 65.0, 68.8)
5. **70.0 - 79.9**: 4 (70.4, 74.9, 73.6)
6. **80.0 - 89.9**: 6 (80.6, 86.2, 86.8, 82.4, 89.2)
7. **90.0 - 99.9**: 2 (90.5)
8. **100.0 - 109.9**: 1 (108.4)
9. **110.0 - 119.9**: 0
10. **120.0 - 129.9**: 0
11. **130.0 - 139.9**: 0
12. **140.0 - 149.9**: 1 (140.7)
### Frequency Distribution Table:
Now, we can summarize this information in a table:
| Class | Frequency |
|--------------------|-----------|
| 30.0 - 39.9 | 4 |
| 40.0 - 49.9 | 5 |
| 50.0 - 59.9 | 8 |
| 60.0 - 69.9 | 5 |
| 70.0 - 79.9 | 4 |
| 80.0 - 89.9 | 6 |
| 90.0 - 99.9 | 2 |
| 100.0 - 109.9 | 1 |
| 110.0 - 119.9 | 0 |
| 120.0 - 129.9 | 0 |
| 130.0 - 139.9 | 0 |
| 140.0 - 149.9 | 1 |
This table summarizes the frequency distribution of the manufacturer's suggested retail prices for BMW automobiles in 2013, using a class width of 10 starting from a lower limit of 30.0.
### Classes:
Using a lower limit of 30.0 and a class width of 10, the classes would be as follows:
1. **30.0 - 39.9**
2. **40.0 - 49.9**
3. **50.0 - 59.9**
4. **60.0 - 69.9**
5. **70.0 - 79.9**
6. **80.0 - 89.9**
7. **90.0 - 99.9**
8. **100.0 - 109.9**
9. **110.0 - 119.9**
10. **120.0 - 129.9**
11. **130.0 - 139.9**
12. **140.0 - 149.9**
### Data:
Here’s the list of the manufacturer’s suggested retail prices (in $1000s) for 2013:
- 50.1
- 70.4
- 55.2
- 56.7
- 74.9
- 55.7
- 55.2
- 64.2
- 39.3
- 80.6
- 36.9
- 108.4
- 47.8
- 90.5
- 47.5
- 73.6
- 38.6
- 47.4
- 30.8
- 86.2
- 60.1
- 89.2
- 59.8
- 68.8
- 65.0
- 86.8
- 140.7
- 82.4
- 62.7
- 53.4
### Tally the Data:
Let's count how many data points fall within each class.
1. **30.0 - 39.9**: 4 (30.8, 36.9, 38.6, 39.3)
2. **40.0 - 49.9**: 5 (47.4, 47.5, 47.8, 50.1)
3. **50.0 - 59.9**: 8 (50.1, 55.2, 55.7, 55.2, 56.7, 53.4)
4. **60.0 - 69.9**: 5 (60.1, 62.7, 64.2, 65.0, 68.8)
5. **70.0 - 79.9**: 4 (70.4, 74.9, 73.6)
6. **80.0 - 89.9**: 6 (80.6, 86.2, 86.8, 82.4, 89.2)
7. **90.0 - 99.9**: 2 (90.5)
8. **100.0 - 109.9**: 1 (108.4)
9. **110.0 - 119.9**: 0
10. **120.0 - 129.9**: 0
11. **130.0 - 139.9**: 0
12. **140.0 - 149.9**: 1 (140.7)
### Frequency Distribution Table:
Now, we can summarize this information in a table:
| Class | Frequency |
|--------------------|-----------|
| 30.0 - 39.9 | 4 |
| 40.0 - 49.9 | 5 |
| 50.0 - 59.9 | 8 |
| 60.0 - 69.9 | 5 |
| 70.0 - 79.9 | 4 |
| 80.0 - 89.9 | 6 |
| 90.0 - 99.9 | 2 |
| 100.0 - 109.9 | 1 |
| 110.0 - 119.9 | 0 |
| 120.0 - 129.9 | 0 |
| 130.0 - 139.9 | 0 |
| 140.0 - 149.9 | 1 |
This table summarizes the frequency distribution of the manufacturer's suggested retail prices for BMW automobiles in 2013, using a class width of 10 starting from a lower limit of 30.0.
Answered by
GPT-4o mini
To create back-to-back stem-and-leaf plots for the given data, we will first group the running times of the movies by their respective stems (the leading digit(s)) and then list the leaves (the last digits) for both PG or PG-13 movies on one side and R-rated movies on the other.
### Data:
**Movies Rated PG or PG-13:**
- 88
- 166
- 112
- 126
- 98
- 108
- 100
- 97
- 145
- 98
- 127
- 115
**Movies Rated R:**
- 88
- 165
- 110
- 122
- 120
- 97
- 118
- 118
- 97
- 157
- 94
- 93
### Step 1: Organize the Data into Stems and Leaves
#### Movies Rated PG or PG-13:
- Stem: 8 | Leaves: 8
- Stem: 9 | Leaves: 7, 8, 8
- Stem: 10 | Leaves: 0, 7, 8
- Stem: 11 | Leaves: 2, 5
- Stem: 12 | Leaves: 6, 7
- Stem: 14 | Leaves: 5
- Stem: 16 | Leaves: 6
#### Movies Rated R:
- Stem: 8 | Leaves: 8
- Stem: 9 | Leaves: 3, 4, 7, 7
- Stem: 10 | Leaves: 0, 8, 8
- Stem: 11 | Leaves: 0, 2, 8, 8
- Stem: 12 | Leaves: 0, 2
- Stem: 15 | Leaves: 7
- Stem: 16 | Leaves: 5
### Step 2: Create the Back-to-Back Stem-and-Leaf Plot
Here is how the back-to-back stem-and-leaf plot will look:
```
Movies Rated R | Movies Rated PG or PG-13
8 | 8 | 8 | 8
9 | 3 4 7 7 | 9 | 7 8 8
10 | 0 8 8 | 10 | 0 7 8
11 | 0 2 8 8 | 11 | 2 5
12 | 0 2 | 12 | 6 7
15 | 7 | 14 | 5
16 | 5 | 16 | 6
```
### Explanation:
- Each row represents a stem (the leading digit), and the leaves (the last digit(s)) are on either side of the central vertical line, showing the distribution of running times for R-rated movies on the left and PG or PG-13 movies on the right.
- The leaves are ordered from smallest to largest within each stem group.
- If there were no movies for a specific stem, that stem would not be included in the plot (it’s not indicated in this diagram since every stem did have leaves).
This visualization allows for quick visual comparison between the running times of the two different rating categories.
### Data:
**Movies Rated PG or PG-13:**
- 88
- 166
- 112
- 126
- 98
- 108
- 100
- 97
- 145
- 98
- 127
- 115
**Movies Rated R:**
- 88
- 165
- 110
- 122
- 120
- 97
- 118
- 118
- 97
- 157
- 94
- 93
### Step 1: Organize the Data into Stems and Leaves
#### Movies Rated PG or PG-13:
- Stem: 8 | Leaves: 8
- Stem: 9 | Leaves: 7, 8, 8
- Stem: 10 | Leaves: 0, 7, 8
- Stem: 11 | Leaves: 2, 5
- Stem: 12 | Leaves: 6, 7
- Stem: 14 | Leaves: 5
- Stem: 16 | Leaves: 6
#### Movies Rated R:
- Stem: 8 | Leaves: 8
- Stem: 9 | Leaves: 3, 4, 7, 7
- Stem: 10 | Leaves: 0, 8, 8
- Stem: 11 | Leaves: 0, 2, 8, 8
- Stem: 12 | Leaves: 0, 2
- Stem: 15 | Leaves: 7
- Stem: 16 | Leaves: 5
### Step 2: Create the Back-to-Back Stem-and-Leaf Plot
Here is how the back-to-back stem-and-leaf plot will look:
```
Movies Rated R | Movies Rated PG or PG-13
8 | 8 | 8 | 8
9 | 3 4 7 7 | 9 | 7 8 8
10 | 0 8 8 | 10 | 0 7 8
11 | 0 2 8 8 | 11 | 2 5
12 | 0 2 | 12 | 6 7
15 | 7 | 14 | 5
16 | 5 | 16 | 6
```
### Explanation:
- Each row represents a stem (the leading digit), and the leaves (the last digit(s)) are on either side of the central vertical line, showing the distribution of running times for R-rated movies on the left and PG or PG-13 movies on the right.
- The leaves are ordered from smallest to largest within each stem group.
- If there were no movies for a specific stem, that stem would not be included in the plot (it’s not indicated in this diagram since every stem did have leaves).
This visualization allows for quick visual comparison between the running times of the two different rating categories.
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