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To create a grouped frequency distribution table, we need to determine an appropriate class interval width. Let's go through the steps:

### Step 1: Find the Range
The range is calculated by subtracting the minimum value from the maximum value.

- Minimum value: 16
- Maximum value: 64

\[
\text{Range} = 64 - 16 = 48
\]

### Step 2: Determine the Number of Classes
A good rule of thumb is to use between 5 and 10 classes. Let's use 7 classes for this example, which is a common choice.

### Step 3: Calculate the Class Width
The class width is found by dividing the range by the number of classes and then rounding up if necessary.

\[
\text{Class Width} = \frac{\text{Range}}{\text{Number of Classes}} = \frac{48}{7} \approx 6.86 \approx 7
\]

### Step 4: Create the Frequency Distribution Table
Using a class width of 7, we'll start the first class at the minimum value (16) and proceed from there.

| Age Group | Frequency |
|-----------|-----------|
| 16 - 22   | 8         |
| 23 - 29   | 7         |
| 30 - 36   | 5         |
| 37 - 43   | 3         |
| 44 - 50   | 2         |
| 51 - 57   | 3         |
| 58 - 64   | 2         |

### Step 5: Analysis of Distribution
From the table, it's clear that tickets are not evenly distributed across the age groups. Younger drivers, particularly those in the 16-22 and 23-29 age groups, received more tickets than older drivers.

### Questions to Explore Further
1. How would the frequency distribution change with a different number of classes?
2. How can we calculate the mean and median age from this data?
3. What other statistical measures could help analyze this distribution?
4. How might the frequency distribution change in different years or locations?
5. What factors could contribute to the high frequency of tickets in younger age groups?

### Tip
Always ensure that your class intervals do not overlap and cover all data points when creating frequency tables.

The following scores are the ages for a random sample of n = 30 drivers who were issued speeding tickets in New York during 2008. Determine the best interval width and place the scores in a grouped frequency distribution table. From looking at your table, does it appear that tickets are issued equally across age groups?

This problem involves creating a grouped frequency distribution table for the ages of drivers who received speeding tickets in New York during 2008. The solution shows how to determine the best class interval width, calculate the range, and analyze the distribution of tickets across different age groups. It is appropriate for students in Grades 9-12.

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