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To solve part (a) of this question, we need to construct a frequency distribution and a relative frequency distribution from the data provided in the table.

### Step 1: Organize the data
The data provided shows the number of "maintenance" activities (from 0 to 5) that each of the 30 people completed. Let’s count the occurrences (frequency) of each possible number (0 through 5).

### Data from the table:
Data entries: 
1, 3, 5, 0, 1, 2, 4, 0, 3, 0, 1, 2, 3, 5, 0, 4, 2, 4, 0, 1, 2, 1, 3, 5, 0, 2, 3, 4, 0, 3

### Step 2: Calculate Frequency \( f \)
Count each number to find the frequency:

- **0** appears 6 times.
- **1** appears 5 times.
- **2** appears 5 times.
- **3** appears 6 times.
- **4** appears 4 times.
- **5** appears 4 times.

So, we have the frequency \( f \) for each number \( x \) as follows:

| Number \( x \) | Frequency \( f \) |
|----------------|--------------------|
| 0              | 6                  |
| 1              | 5                  |
| 2              | 5                  |
| 3              | 6                  |
| 4              | 4                  |
| 5              | 4                  |

### Step 3: Calculate Relative Frequency \( \frac{f}{n} \)
The relative frequency is found by dividing each frequency \( f \) by the total number of observations \( n = 30 \).

| Number \( x \) | Frequency \( f \) | Relative Frequency \( \frac{f}{n} \) (%) |
|----------------|--------------------|------------------------------------------|
| 0              | 6                  | \( \frac{6}{30} \times 100 = 20\% \)    |
| 1              | 5                  | \( \frac{5}{30} \times 100 = 17\% \)    |
| 2              | 5                  | \( \frac{5}{30} \times 100 = 17\% \)    |
| 3              | 6                  | \( \frac{6}{30} \times 100 = 20\% \)    |
| 4              | 4                  | \( \frac{4}{30} \times 100 = 13\% \)    |
| 5              | 4                  | \( \frac{4}{30} \times 100 = 13\% \)    |

### Final Table
The completed table with both frequency and relative frequency distributions:

| Number \( x \) | Frequency \( f \) | Relative Frequency (%) |
|----------------|--------------------|-------------------------|
| 0              | 6                  | 20%                     |
| 1              | 5                  | 17%                     |
| 2              | 5                  | 17%                     |
| 3              | 6                  | 20%                     |
| 4              | 4                  | 13%                     |
| 5              | 4                  | 13%                     |

Would you like more details on any step, or do you have further questions?

### Related Questions
1. How would the distribution change if there were additional people in the survey?
2. What does the relative frequency tell us about the data?
3. How could this data be represented in a bar graph?
4. What are other ways to visualize frequency distributions?
5. How does the frequency distribution relate to measures like the mean or median?

### Tip
Always double-check your total frequency count to ensure it matches the number of data points given. This confirms the accuracy of your calculations.

Construct frequency and relative frequency distributions based on the number of 'maintenance' activities (0-5) completed by 30 people, as shown in the data table.

Learn how to construct frequency and relative frequency distributions based on a data set of maintenance activities completed by 30 people. This exercise includes calculating both frequency and relative frequency percentages, and is ideal for students in Grades 8-10.

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