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The following scores are the ages for a random sample of n = 32 drivers who were issued parking tickets in Chicago during 2015.
57, 30, 45, 59, 39, 53, 28, 19,
34, 21, 34, 38, 52, 29, 64, 39,
22, 44, 46, 26, 56, 20, 33, 58,
32, 25, 48, 22, 51, 26, 63, 51
Determine the best interval width and identify the approximate number of intervals needed for a grouped frequency distribution table.
Use an interval width of ________   years, requiring about ________ intervals.

To determine the best interval width and the approximate number of intervals for a grouped frequency distribution, we will follow these steps:

1. **Find the range of the dataTo determine the best interval width and the approximate number of intervals for a grouped frequency distribution, we will follow these steps:

1. **Find the range of the **
   - Range = Maximum value - Minimum value

2. **Determine a suitable interval width:**
   - A good rule of thumb is to aim for around 5 to 20 intervals.
   - The interval width can be calculated by dividing the range by the desired number of intervals and then rounding up to a convenient number.

3. **Determine the number of intervals needed:**
   - The number of intervals is calculated by dividing the range by the interval width.

### Step 1: Find the Range
The ages provided are:
- Minimum value = 19
- Maximum value = 64

Range = 64 - 19 = 45 years

### Step 2: Determine a Suitable Interval Width
Let's try with an approximate number of 6 to 10 intervals.

#### Test with 6 intervals:
Interval width ≈ Range / Number of intervals = 45 / 6 ≈ 7.5 ≈ 8 years (rounded up)

#### Test with 8 intervals:
Interval width ≈ Range / Number of intervals = 45 / 8 ≈ 5.625 ≈ 6 years (rounded up)

### Step 3: Determine the Number of Intervals
For an interval width of 8 years:
Number of intervals ≈ Range / Interval width = 45 / 8 ≈ 5.625 ≈ 6 intervals

For an interval width of 6 years:
Number of intervals ≈ Range / Interval width = 45 / 6 ≈ 7.5 ≈ 8 intervals

### Conclusion
Using an interval width of **6 years** will require about **8 intervals**.

Would you like a detailed explanation of how these steps were carried out, or do you have any specific questions?

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**Relative Questions:**

1. What is the significance of choosing an appropriate interval width in a frequency distribution table?
2. How does the range of the data affect the number of intervals needed?
3. Why is it necessary to round the interval width to a convenient number?
4. Can you describe a situation where a smaller number of intervals might be more appropriate?
5. What could be the consequences of using too many intervals in a frequency distribution table?

**Tip:** When constructing a grouped frequency distribution, ensure that the intervals are mutually exclusive and cover the entire range of the data without overlap.

Learn how to determine the best interval width and the approximate number of intervals for a frequency distribution table using statistical methods. This problem involves calculating the range of data and selecting an appropriate interval width. Suitable for students and professionals interested in statistics and data analysis.

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