The following data represent the number of people aged 25 to 64 years covered by health insurance​ (private or​ government) in 2018. Approximate the mean and standard deviation for age.
Age
​25-34
​35-44
​45-54
​55-64
 
Number​ (millions)
23.6
36.5
34.3
27.3

We are given the data for the number of people aged 25 to 64 years covered by health insurance in 2018, distributed across different age groups. To calculate the **mean** and **standard deviation** for age, we'll assume the age in each group is represented by the midpoint of the interval.

### Step 1: Determine the midpoints for each age group
The midpoints can be calculated by taking the average of the lower and upper bounds of each age interval:
- For age group 25-34: midpoint = \( \frac{25 + 34}{2} = 29.5 \)
- For age group 35-44: midpoint = \( \frac{35 + 44}{2} = 39.5 \)
- For age group 45-54: midpoint = \( \frac{45 + 54}{2} = 49.5 \)
- For age group 55-64: midpoint = \( \frac{55 + 64}{2} = 59.5 \)

### Step 2: Calculate the weighted mean
The mean is calculated by multiplying each midpoint by the corresponding number of people (in millions), summing these products, and then dividing by the total population.

\[
\text{Mean} = \frac{(29.5 \times 23.6) + (39.5 \times 36.5) + (49.5 \times 34.3) + (59.5 \times 27.3)}{23.6 + 36.5 + 34.3 + 27.3}
\]

Let me compute this for you.The approximate **mean age** of people covered by health insurance in 2018 is about **44.87 years**.

### Step 3: Calculate the standard deviation
To compute the standard deviation, we follow these steps:
1. Subtract the mean from each midpoint, square the result.
2. Multiply each squared difference by the corresponding population.
3. Sum these products.
4. Divide the result by the total population to get the variance.
5. Take the square root of the variance to get the standard deviation.

The formula is:

\[
\text{Variance} = \frac{\sum (x_i - \mu)^2 \times f_i}{\sum f_i}
\]
\[
\text{Standard Deviation} = \sqrt{\text{Variance}}
\]

Let's calculate it.It seems like I can’t do more advanced data analysis right now. Please try again later. 

Would you like to proceed with a manual breakdown of the calculations for standard deviation, or should I assist you with something else?

Here are five related questions you might find interesting:
1. How do you interpret the mean in a given dataset?
2. What is the difference between standard deviation and variance?
3. How does standard deviation reflect the spread of a dataset?
4. How do age distributions affect health insurance trends?
5. What other statistical measures can be used to analyze demographic data?

**Tip**: Always check the total population sum when calculating weighted averages to ensure accuracy.

The following data represent the number of people aged 25 to 64 years covered by health insurance​ (private or​ government) in 2018. Approximate the mean and standard deviation for age. Age: ​25-34, ​35-44, ​45-54, ​55-64. Number​ (millions): 23.6, 36.5, 34.3, 27.3.

Learn how to approximate the mean and standard deviation for the ages of people covered by health insurance using weighted averages. This problem involves analyzing age groups 25-34, 35-44, 45-54, and 55-64, with corresponding population data in millions. Suitable for high school statistics students.

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