Step 1: Create a Frequency Distribution Table

First, we'll organize the given data into a frequency distribution table with age groups, midpoints, frequencies (in millions), and relative frequencies.

Age Group	Midpoint (x)	Population (in millions) (f)	Relative Frequency (%)
Under 4 years	2	23.5	7
5-14 years	9.5	45.9	13
15-19 years	17	22.8	7
20-24 years	22	24.3	7
25-34 years	29.5	54.4	16
35-44 years	39.5	37.3	11
45-64 years	54.5	79.5	23
65 years and over	70	56.1	16

Step 2: Calculate the Sample Mean

The formula for the sample mean is:

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

Where:

• $f$ = frequency (population in millions)
• $x$ = midpoint of each age group

Now, calculate the sum of $f \cdot x$ and the sum of $f$:

$\sum (f \cdot x) = (23.5 \cdot 2) + (45.9 \cdot 9.5) + (22.8 \cdot 17) + (24.3 \cdot 22) + (54.4 \cdot 29.5) + (37.3 \cdot 39.5) + (79.5 \cdot 54.5) + (56.1 \cdot 70)$

$\sum f = 23.5 + 45.9 + 22.8 + 24.3 + 54.4 + 37.3 + 79.5 + 56.1$

Let’s calculate these values.

It seems like I can’t do more advanced data analysis right now. Please try again later. If you'd like, I can guide you through the manual steps or provide more help with specific parts of the problem.

Would you like assistance with:

1. Manually calculating the sum of $f \cdot x$?
2. Calculating the sample standard deviation?
3. Understanding frequency distribution tables?
4. Clarifying how to compute midpoints?
5. General questions on calculating means and standard deviations?

Tip: Always double-check that your midpoints represent the central value of each interval.