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:

Step 3: Calculate Relative Frequency $\frac{f}{n}$

The relative frequency is found by dividing each frequency $f$ by the total number of observations $n = 30$.

Final Table

The completed table with both frequency and relative frequency distributions:

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.