Questions: 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): 23.7, 39.9, 37.6, 22.3 μ = 44.74 σ = (Type an integer or decimal rounded to two decimal places as needed.)

Solution Steps

To find the mean age \( \mu \), we use the formula:

\[ \mu = \frac{\sum x_i}{n} \]

where \( x_i \) represents the midpoints of the age groups and \( n \) is the total number of individuals.

Calculating the weighted sum:

\[ \sum x_i = 5359.5 \quad \text{and} \quad n = 121 \]

Thus, the mean age is:

\[ \mu = \frac{5359.5}{121} \approx 44.29 \]

The variance \( \sigma^2 \) is calculated using the formula:

\[ \sigma^2 = \frac{\sum (x_i - \mu)^2}{n} \]

From the calculations, we find:

\[ \sigma^2 = 99.34 \]

The standard deviation \( \sigma \) is the square root of the variance:

\[ \sigma = \sqrt{99.34} \approx 9.97 \]

Final Answer