To construct a relative frequency distribution for the 2012 vehicle sales, we first need to calculate the total number of vehicles sold in 2012 across all manufacturers.
Step 1: Calculate Total Sales for 2012
- General Motors: 208,489
- Ford: 177,806
- Chrysler LLC: 131,409
- Toyota: 159,752
- Honda: 108,531
- Nissan: 105,953
Total Sales in 2012:
\[ 208,489 + 177,806 + 131,409 + 159,752 + 108,531 + 105,953 = 891,940 \]
Step 2: Calculate the Relative Frequencies
Now, we will calculate the relative frequency for each manufacturer by dividing the number of vehicles sold by the total vehicles sold in 2012.
\[ \text{Relative Frequency} = \frac{\text{Number of Vehicles Sold}}{\text{Total Sales}} \]
Calculations:
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General Motors: \[ \text{Relative Frequency} = \frac{208,489}{891,940} \approx 0.233 \]
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Ford: \[ \text{Relative Frequency} = \frac{177,806}{891,940} \approx 0.199 \]
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Chrysler LLC: \[ \text{Relative Frequency} = \frac{131,409}{891,940} \approx 0.147 \]
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Toyota: \[ \text{Relative Frequency} = \frac{159,752}{891,940} \approx 0.179 \]
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Honda: \[ \text{Relative Frequency} = \frac{108,531}{891,940} \approx 0.122 \]
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Nissan: \[ \text{Relative Frequency} = \frac{105,953}{891,940} \approx 0.119 \]
Step 3: Present the Relative Frequency Distribution
Now we can summarize the results in a table format.
| Manufacturer | Vehicles Sold (2012) | Relative Frequency | |--------------------|----------------------|--------------------| | General Motors | 208,489 | 0.233 | | Ford | 177,806 | 0.199 | | Chrysler LLC | 131,409 | 0.147 | | Toyota | 159,752 | 0.179 | | Honda | 108,531 | 0.122 | | Nissan | 105,953 | 0.119 | | Total | 891,940 | 1.000 |
Note
The relative frequencies have been rounded to three decimal places as requested.
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