he estimated distribution​ (in millions) of the population by age in a certain country for the year 2015 is shown in the pie chart. Make a frequency distribution for the data. Then use the table to estimate the sample mean and the sample standard deviation of the data set. Use 70 as the midpoint for​ "65 years and​ over."
An untitled circle graph is divided into eight sectors with labels and approximate sizes as a percentage of a circle as follows: Under 4 years, 23.5, 7 percent; 5 to 14 years, 45.9, 13 percent; 15 to 19 years, 22.8, 7 percent; 20 to 24 years, 24.3, 7 percent; 25 to 34 years, 54.4, 16 percent; 35 to 44 years, 37.3, 11 percent; 45 to 65 years, 79.5, 23 percent; 65 years and over, 56.1, 16 percent.
Under 4 years:  23.5
5-14 years:  45.9
15-19 years:  22.8
20-24 years:  24.3
25-34 years:  54.4
35-44 years:  37.3
45-64 years:  79.5
65 years and over:  56.1

### 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.

The estimated distribution​ (in millions) of the population by age in a certain country for the year 2015 is shown in the pie chart. Make a frequency distribution for the data. Then use the table to estimate the sample mean and the sample standard deviation of the data set. Use 70 as the midpoint for​ '65 years and​ over.' An untitled circle graph is divided into eight sectors with labels and approximate sizes as a percentage of a circle as follows: Under 4 years, 23.5, 7 percent; 5 to 14 years, 45.9, 13 percent; 15 to 19 years, 22.8, 7 percent; 20 to 24 years, 24.3, 7 percent; 25 to 34 years, 54.4, 16 percent; 35 to 44 years, 37.3, 11 percent; 45 to 65 years, 79.5, 23 percent; 65 years and over, 56.1, 16 percent.

This problem focuses on creating a frequency distribution for a population in millions by age group in 2015, calculating the sample mean, and estimating the sample standard deviation. Key mathematical concepts include frequency distributions, means, and standard deviations, suitable for students in Grades 10-12.

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