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Based on the image provided, it contains a frequency distribution table for savings among a random sample of 25-34 year-olds and a request to approximate the mean and standard deviation of the amount saved.

Here’s how the values are computed:

### Frequency Table Summary:
| Savings Range | Frequency |
|---------------|-----------|
| $0–$199       | 338       |
| $200–$399     | 97        |
| $400–$599     | 49        |
| $600–$799     | 24        |
| $800–$999     | 10        |
| $1000–$1199   | 6         |
| $1200–$1399   | 1         |

### To approximate the mean and standard deviation:
1. **Estimate the midpoint for each savings range**:
   - $0–$199: Midpoint = $99.50
   - $200–$399: Midpoint = $299.50
   - $400–$599: Midpoint = $499.50
   - $600–$799: Midpoint = $699.50
   - $800–$999: Midpoint = $899.50
   - $1000–$1199: Midpoint = $1099.50
   - $1200–$1399: Midpoint = $1299.50

2. **Multiply the midpoint by the corresponding frequency** for each range to get the total contribution to the savings.

3. **Sum all the contributions and divide by the total frequency** to get the **mean**.

4. For the **standard deviation**, use the formula:
   \[
   \sigma = \sqrt{\frac{\sum (f \cdot (x - \bar{x})^2)}{n-1}}
   \]
   Where:
   - $ f $ is the frequency,
   - $ x $ is the midpoint,
   - $ \bar{x} $ is the mean,
   - $ n $ is the total number of frequencies.

### Sample Mean: $230
### Sample Standard Deviation: $219

These are the approximated values as per the request.

Would you like a more detailed breakdown of the calculations or to confirm any further steps?

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Here are 5 related questions that could extend your understanding:
1. How would the mean change if the savings ranges were wider?
2. How does the standard deviation reflect the spread of savings amounts?
3. What is the significance of rounding in statistical calculations?
4. How would you calculate the variance from the given data?
5. How can we interpret the midpoint assumption for skewed distributions?

**Tip**: Always check the class intervals in frequency distributions, as they can influence the accuracy of the mean and standard deviation calculations.

A random sample of 25–34 year-olds was asked, 'How much do you currently have in savings, not including retirement savings?' The frequency distribution of the data is provided. Approximate the mean and standard deviation of the savings data.

Learn how to calculate the mean and standard deviation from a frequency distribution using a dataset on savings among 25-34 year-olds. The table includes ranges from $0 to $1399, and the sample mean is $230, with a standard deviation of $219.

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