https://file.aiquickdraw.com/mathbot/file/1726024294768u1pa3tmp.jpg

To construct the frequency distribution, we'll need to follow these steps:

1. **Determine the class intervals** based on the given class width of 0.75 and the lower limit of 0.00.
2. **Count the frequency** of the data values falling within each class interval.

The class intervals based on the given width (0.75) and starting from 0.00 would be:

1. 0.00 - 0.74
2. 0.75 - 1.49
3. 1.50 - 2.24
4. 2.25 - 2.99
5. 3.00 - 3.74
6. 3.75 - 4.49
7. 4.50 - 5.24
8. 5.25 - 5.99
9. 6.00 - 6.74

I'll count the number of data points in each interval to complete the frequency distribution.

Let's start by counting the frequencies for each class.Here is the frequency distribution based on the class intervals:

1. **0.00 - 0.74**: 6
2. **0.75 - 1.49**: 20
3. **1.50 - 2.24**: 10
4. **2.25 - 2.99**: 7
5. **3.00 - 3.74**: 12
6. **3.75 - 4.49**: 3
7. **4.50 - 5.24**: 1
8. **5.25 - 5.99**: 1
9. **6.00 - 6.74**: 1

This distribution summarizes the number of vehicles within each particulate emission range.

Would you like any additional details or help with anything else?

### Relative Questions:
1. How is the class width determined for a frequency distribution?
2. Why is it important to have non-overlapping class intervals?
3. How can a histogram be used to visualize this frequency distribution?
4. What is the difference between a frequency distribution and a relative frequency distribution?
5. How might the frequency distribution change with a different class width?

### Tip:
When constructing a frequency distribution, ensure that the sum of all frequencies equals the total number of observations to verify accuracy.

The data in the following table are particulate emissions for 65 vehicles, in units of grams of particles per gallon of fuel. Construct a frequency distribution for the data using a class width of 0.75, and using 0.00 as the lower limit for the first class.

Solve a frequency distribution problem involving the particulate emissions of 65 vehicles. Learn how to construct a frequency table with a class width of 0.75, starting from 0.00 as the lower limit, and identify the number of vehicles in each class.

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