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Sagot :
To solve the problem of computing the row percentages for each automobile make based on their average speeds, we need to follow these steps:
1. Determine the total number of wins for each make.
2. Calculate the percentage of wins within each speed category for each make.
Based on the provided table in the question, here is the cross-tabulation data:
| Make | [tex]\(130-139.9\)[/tex] | [tex]\(140-149.9\)[/tex] | [tex]\(150-159.9\)[/tex] | [tex]\(160-169.9\)[/tex] | [tex]\(170-179.9\)[/tex] | Total |
|-----------|---------------|---------------|---------------|---------------|---------------|-------|
| Buick | 1 | 0 | 0 | 0 | 0 | 1 |
| Chevrolet | 3 | 5 | 4 | 3 | 1 | 16 |
| Dodge | 2 | 2 | 2 | 1 | 0 | 7 |
| Ford | 0 | 1 | 0 | 0 | 0 | 1 |
| Total | 6 | 8 | 6 | 4 | 1 | 25 |
Now, we proceed to compute the row percentages for each automobile make:
1. Buick:
- Total: 1
- Percentage for [tex]\(130-139.9\)[/tex] MPH: [tex]\(\frac{1}{1} \times 100 = 100.0\%\)[/tex]
- Percentage for other speed categories: [tex]\(0 / 1 \times 100 = 0.0\%\)[/tex] (because there were no wins in other categories).
2. Chevrolet:
- Total: 16
- Percentage for [tex]\(130-139.9\)[/tex] MPH: [tex]\(\frac{3}{16} \times 100 = 18.75\%\)[/tex]
- Percentage for [tex]\(140-149.9\)[/tex] MPH: [tex]\(\frac{5}{16} \times 100 = 31.25\%\)[/tex]
- Percentage for [tex]\(150-159.9\)[/tex] MPH: [tex]\(\frac{4}{16} \times 100 = 25.0\%\)[/tex]
- Percentage for [tex]\(160-169.9\)[/tex] MPH: [tex]\(\frac{3}{16} \times 100 = 18.75\%\)[/tex]
- Percentage for [tex]\(170-179.9\)[/tex] MPH: [tex]\(\frac{1}{16} \times 100 = 6.25\%\)[/tex]
3. Dodge:
- Total: 7
- Percentage for [tex]\(130-139.9\)[/tex] MPH: [tex]\(\frac{2}{7} \times 100 = 28.57\%\)[/tex]
- Percentage for [tex]\(140-149.9\)[/tex] MPH: [tex]\(\frac{2}{7} \times 100 = 28.57\%\)[/tex]
- Percentage for [tex]\(150-159.9\)[/tex] MPH: [tex]\(\frac{2}{7} \times 100 = 28.57\%\)[/tex]
- Percentage for [tex]\(160-169.9\)[/tex] MPH: [tex]\(\frac{1}{7} \times 100 = 14.29\%\)[/tex]
- Percentage for [tex]\(170-179.9\)[/tex] MPH: [tex]\(\frac{0}{7} \times 100 = 0.0\%\)[/tex]
4. Ford:
- Total: 1
- Percentage for [tex]\(140-149.9\)[/tex] MPH: [tex]\(\frac{1}{1} \times 100 = 100.0\%\)[/tex]
- Percentage for other speed categories: [tex]\(0 / 1 \times 100 = 0.0\%\)[/tex] (because there was only one win in the [tex]\(140-149.9\)[/tex] MPH category).
The final row percentages table would look like this:
| Make | [tex]\(130-139.9\)[/tex] | [tex]\(140-149.9\)[/tex] | [tex]\(150-159.9\)[/tex] | [tex]\(160-169.9\)[/tex] | [tex]\(170-179.9\)[/tex] |
|-----------|---------------|---------------|---------------|---------------|---------------|
| Buick | 100.0 | 0.0 | 0.0 | 0.0 | 0.0 |
| Chevrolet | 18.75 | 31.25 | 25.0 | 18.75 | 6.25 |
| Dodge | 28.57 | 28.57 | 28.57 | 14.29 | 0.0 |
| Ford | 0.0 | 100.0 | 0.0 | 0.0 | 0.0 |
These percentages represent the distribution of wins within each speed category for the specified automobile makes from 1988 to 2012.
1. Determine the total number of wins for each make.
2. Calculate the percentage of wins within each speed category for each make.
Based on the provided table in the question, here is the cross-tabulation data:
| Make | [tex]\(130-139.9\)[/tex] | [tex]\(140-149.9\)[/tex] | [tex]\(150-159.9\)[/tex] | [tex]\(160-169.9\)[/tex] | [tex]\(170-179.9\)[/tex] | Total |
|-----------|---------------|---------------|---------------|---------------|---------------|-------|
| Buick | 1 | 0 | 0 | 0 | 0 | 1 |
| Chevrolet | 3 | 5 | 4 | 3 | 1 | 16 |
| Dodge | 2 | 2 | 2 | 1 | 0 | 7 |
| Ford | 0 | 1 | 0 | 0 | 0 | 1 |
| Total | 6 | 8 | 6 | 4 | 1 | 25 |
Now, we proceed to compute the row percentages for each automobile make:
1. Buick:
- Total: 1
- Percentage for [tex]\(130-139.9\)[/tex] MPH: [tex]\(\frac{1}{1} \times 100 = 100.0\%\)[/tex]
- Percentage for other speed categories: [tex]\(0 / 1 \times 100 = 0.0\%\)[/tex] (because there were no wins in other categories).
2. Chevrolet:
- Total: 16
- Percentage for [tex]\(130-139.9\)[/tex] MPH: [tex]\(\frac{3}{16} \times 100 = 18.75\%\)[/tex]
- Percentage for [tex]\(140-149.9\)[/tex] MPH: [tex]\(\frac{5}{16} \times 100 = 31.25\%\)[/tex]
- Percentage for [tex]\(150-159.9\)[/tex] MPH: [tex]\(\frac{4}{16} \times 100 = 25.0\%\)[/tex]
- Percentage for [tex]\(160-169.9\)[/tex] MPH: [tex]\(\frac{3}{16} \times 100 = 18.75\%\)[/tex]
- Percentage for [tex]\(170-179.9\)[/tex] MPH: [tex]\(\frac{1}{16} \times 100 = 6.25\%\)[/tex]
3. Dodge:
- Total: 7
- Percentage for [tex]\(130-139.9\)[/tex] MPH: [tex]\(\frac{2}{7} \times 100 = 28.57\%\)[/tex]
- Percentage for [tex]\(140-149.9\)[/tex] MPH: [tex]\(\frac{2}{7} \times 100 = 28.57\%\)[/tex]
- Percentage for [tex]\(150-159.9\)[/tex] MPH: [tex]\(\frac{2}{7} \times 100 = 28.57\%\)[/tex]
- Percentage for [tex]\(160-169.9\)[/tex] MPH: [tex]\(\frac{1}{7} \times 100 = 14.29\%\)[/tex]
- Percentage for [tex]\(170-179.9\)[/tex] MPH: [tex]\(\frac{0}{7} \times 100 = 0.0\%\)[/tex]
4. Ford:
- Total: 1
- Percentage for [tex]\(140-149.9\)[/tex] MPH: [tex]\(\frac{1}{1} \times 100 = 100.0\%\)[/tex]
- Percentage for other speed categories: [tex]\(0 / 1 \times 100 = 0.0\%\)[/tex] (because there was only one win in the [tex]\(140-149.9\)[/tex] MPH category).
The final row percentages table would look like this:
| Make | [tex]\(130-139.9\)[/tex] | [tex]\(140-149.9\)[/tex] | [tex]\(150-159.9\)[/tex] | [tex]\(160-169.9\)[/tex] | [tex]\(170-179.9\)[/tex] |
|-----------|---------------|---------------|---------------|---------------|---------------|
| Buick | 100.0 | 0.0 | 0.0 | 0.0 | 0.0 |
| Chevrolet | 18.75 | 31.25 | 25.0 | 18.75 | 6.25 |
| Dodge | 28.57 | 28.57 | 28.57 | 14.29 | 0.0 |
| Ford | 0.0 | 100.0 | 0.0 | 0.0 | 0.0 |
These percentages represent the distribution of wins within each speed category for the specified automobile makes from 1988 to 2012.
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