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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. 

Let's complete the steps to determine the interval width and the number of intervals needed for the grouped frequency distribution table.

### Data Summary:
The provided ages are:

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  

### Step 1: Range of Data
- **Minimum age** = 19
- **Maximum age** = 64

**Range** = 64 - 19 = 45 years

### Step 2: Determine the Interval Width
We aim for 6 to 10 intervals:

#### 6 Intervals
- **Interval width** = 45 / 6 ≈ 7.5 years → rounded to **8 years**.

#### 8 Intervals
- **Interval width** = 45 / 8 ≈ 5.625 years → rounded to **6 years**.

### Step 3: Number of Intervals
- **With interval width of 8 years**: 
  - Number of intervals = 45 / 8 ≈ 6 intervals.
- **With interval width of 6 years**: 
  - Number of intervals = 45 / 6 ≈ 8 intervals.

### Conclusion
The best interval width would be **6 years**, requiring about **8 intervals**.

If you need any further details or have additional questions, feel free to ask!

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**Relative Questions:**

1. How does the choice of interval width affect the readability of the frequency distribution?
2. Why might you choose a wider interval over a narrower one?
3. Can you explain how rounding affects the calculation of interval widths?
4. What are the advantages of using approximately 8 intervals for this data set?
5. How might the shape of the frequency distribution change with a different number of intervals?

**Tip:** Always ensure that the chosen intervals are consistent across the range of data to maintain accuracy and avoid overlapping.

Learn how to determine the best interval width and the number of intervals needed for a grouped frequency distribution table using statistical data analysis techniques. This problem involves calculating range, choosing suitable intervals, and ensuring accuracy in frequency distribution. Suitable for students and professionals interested in statistical analysis.

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