QuestionRecently, a random sample of 25-34 year olds was asked, "How much do you currently have in savings, not including retirement savings?" The data in the table represent the responses to the survey. Approximate the mean and standard deviation amount of savings.
Click the icon to view the frequency distribution for the amount of savings.
The sample mean amount of savings is $\$$ $\square$ . (Round to the nearest dollar as needed.)
Frequency distribution of amount of savings \begin{tabular}{cc} Savings & Frequency \\ \hline$\$ 0-\$ 199$ & 339 \\ \hline$\$ 200-\$ 399$ & 89 \\ \hline$\$ 400-\$ 599$ & 62 \\ \hline$\$ 600-\$ 799$ & 16 \\ \hline$\$ 800-\$ 999$ & 11 \\ \hline$\$ 1000-\$ 1199$ & 7 \\ \hline$\$ 1200-\$ 1399$ & 1 \\ \hline \end{tabular} Print Done

Studdy Solution
Calculate the weighted standard deviation using the midpoints, frequencies, and the mean:
$\text{Variance} = \frac{\sum (\text{frequency} \times (\text{midpoint} - \text{mean})^2)}{\sum \text{frequency}}$
$= \frac{(339 \times (99.5 - 229.46)^2) + (89 \times (299.5 - 229.46)^2) + (62 \times (499.5 - 229.46)^2) + (16 \times (699.5 - 229.46)^2) + (11 \times (899.5 - 229.46)^2) + (7 \times (1099.5 - 229.46)^2) + (1 \times (1299.5 - 229.46)^2)}{525}$
Calculate each term and sum them, then divide by 525 to find the variance. Take the square root to find the standard deviation.
The sample mean amount of savings is $\boxed{229}$.