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Let's go through the questions step by step from the image.

### 1. Data given:
The data represents the travel time to work for 40 workers (in minutes):
```
34, 35, 42, 52, 65, 20, 60, 49, 38, 37, 23, 24, 35, 59, 62, 48, 52,
41, 45, 28, 47, 50, 47, 58, 30, 32, 48, 40, 45, 59, 55, 50, 47, 40, 
30, 28, 45, 56, 62, 50
```

### Part (a): Find the Range
The range of a data set is calculated as the difference between the maximum and minimum values.

- **Maximum value**: 65
- **Minimum value**: 20

So, the range is:
\[
\text{Range} = 65 - 20 = 45
\]

### Part (b): Find the Class Width
To find the class width for a frequency distribution with 5 classes:
1. **Range** = 45 (calculated from part a)
2. **Number of classes** = 5

The formula for class width is:
\[
\text{Class width} = \frac{\text{Range}}{\text{Number of classes}} = \frac{45}{5} = 9
\]
Thus, the class width is **9**.

### Part (c): Complete the Frequency Distribution Table
The minimum value of the dataset is 20, and the class width is 9. We can now construct the class intervals. Let's define the classes, midpoints, and frequencies.

| Class Boundaries | Midpoint | Frequency | Cumulative Frequency | Relative Frequency | Percentage Frequency |
|------------------|----------|-----------|----------------------|--------------------|----------------------|
| 20 - 28          | 24       | 7         | 7                    | 0.175              | 17.5%                |
| 29 - 37          | 33       | 9         | 16                   | 0.225              | 22.5%                |
| 38 - 46          | 42       | 10        | 26                   | 0.250              | 25%                  |
| 47 - 55          | 51       | 9         | 35                   | 0.225              | 22.5%                |
| 56 - 64          | 60       | 5         | 40                   | 0.125              | 12.5%                |

Explanation:
- **Class Boundaries**: These are determined using the class width of 9 starting from the minimum value (20).
- **Midpoint**: Midpoint of each class is \((\text{Lower limit} + \text{Upper limit}) / 2\).
- **Frequency**: Number of data points that fall within each class boundary.
- **Cumulative Frequency**: Running total of the frequencies.
- **Relative Frequency**: Frequency divided by the total number of observations (40).
- **Percentage Frequency**: Relative frequency multiplied by 100.

### Part (d): Draw the Relative Histogram
To draw the relative histogram:
- The x-axis will represent the class intervals (20-28, 29-37, etc.).
- The y-axis will represent the relative frequencies.
Each bar will have a height corresponding to the relative frequency of each class.

### Part (e): Draw the Ogive
An ogive (cumulative frequency graph) is a line graph of the cumulative frequency:
- Plot the cumulative frequency against the upper class boundaries.
- Connect the points to form the graph.

---

Would you like a detailed explanation of any part or a graph plotted for the histogram or ogive?

Here are five related questions:
1. How do you calculate the midpoint for each class?
2. What does cumulative frequency represent, and how is it useful?
3. How do you determine the number of classes for a frequency distribution?
4. What is the difference between relative and absolute frequency?
5. How do you use an ogive to estimate the median or percentiles?

**Tip**: Always check that the sum of frequencies equals the total number of observations to verify your frequency distribution table.

Forty workers were randomly surveyed about how long it takes them to travel to work each day. The data below are given in minutes: 34, 35, 42, 52, 65, 20, 60, 49, 38, 37, 23, 24, 35, 59, 62, 48, 52, 41, 45, 28, 47, 50, 47, 58, 30, 32, 48, 40, 45, 59, 55, 50, 47, 40, 30, 28, 45, 56, 62, 50. Find the range, class width, and complete the frequency distribution table, draw a relative histogram, and an ogive.

Solve a statistics problem involving travel time data for 40 workers. Learn how to find the range, class width, complete a frequency distribution table, and create a relative histogram and ogive. Includes key concepts like cumulative frequency and percentage frequency.

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