To calculate the approximate mean age from the given frequency distribution, we can use the formula for the weighted mean:

$\text{Mean} = \frac{\sum (f \cdot x)}{\sum f}$

Where:

• $f$ is the frequency of each age group (the number of people in each age group).
• $x$ is the midpoint of each class (the average age for each group).
• $\sum f$ is the sum of all the frequencies.

Steps:

1. Find the midpoint of each age group.

   • For the group $0-9$, the midpoint is $\frac{0 + 9}{2} = 4.5$.
   • Similarly, for each other group, find the midpoint.

2. Multiply each midpoint by the corresponding frequency to find $f \cdot x$.

3. Sum the values of $f \cdot x$ for all the groups.

4. Sum the frequencies.

5. Calculate the mean using the formula.

Let's go through these steps and calculate the mean.The approximate mean age of the residents is $27.8$ years (rounded to one decimal place).

Would you like further details or clarifications? Here are five related questions to consider:

1. How would the mean age change if a different age group had a significantly larger population?
2. Can the median age be calculated using the given data?
3. How does the frequency distribution affect the calculation of the mean?
4. What is the difference between mean, median, and mode in this context?
5. How can the weighted mean formula be applied in other fields like economics?

Tip: The midpoint of a class interval is a critical component when working with frequency distributions and approximations. Always double-check it for accuracy!