https://file.aiquickdraw.com/mathbot/file/1725480217845jvue4ubb.jpg

​Recently, 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.


To calculate the approximate mean and standard deviation of the savings amounts from the data provided, we'll need to follow these steps:

### 1. **Midpoint Calculation:**
   For each savings range, calculate the midpoint. The midpoint ($x_i$) of each class interval is calculated as:
   \[
   \text{Midpoint} = \frac{\text{Lower limit} + \text{Upper limit}}{2}
   \]
   
### 2. **Mean Calculation:**
   The mean ($\mu$) is calculated using the formula:
   \[
   \mu = \frac{\sum (f_i \times x_i)}{\sum f_i}
   \]
   Where:
   - $f_i$ is the frequency of each class interval.
   - $x_i$ is the midpoint of each class interval.

### 3. **Standard Deviation Calculation:**
   The standard deviation ($\sigma$) is calculated using the formula:
   \[
   \sigma = \sqrt{\frac{\sum f_i (x_i - \mu)^2}{\sum f_i}}
   \]
   
Now let's proceed with these calculations using the provided dataTo calculate the approximate mean and standard deviation of the savings amounts from the data provided, we'll need to follow these steps:

### 1. **Midpoint Calculation:**
   For each savings range, calculate the midpoint. The midpoint ($x_i$) of each class interval is calculated as:
   \[
   \text{Midpoint} = \frac{\text{Lower limit} + \text{Upper limit}}{2}
   \]
   
### 2. **Mean Calculation:**
   The mean ($\mu$) is calculated using the formula:
   \[
   \mu = \frac{\sum (f_i \times x_i)}{\sum f_i}
   \]
   Where:
   - $f_i$ is the frequency of each class interval.
   - $x_i$ is the midpoint of each class interval.

### 3. **Standard Deviation Calculation:**
   The standard deviation ($\sigma$) is calculated using the formula:
   \[
   \sigma = \sqrt{\frac{\sum f_i (x_i - \mu)^2}{\sum f_i}}
   \]
   
Now let's proceed with these calculations using the provided 

| Savings    | Frequency ($f_i$) | Midpoint ($x_i$) |
|------------|--------------------|--------------------|
| $0 - $199  | 349                | $ \frac{0 + 199}{2} = 99.5 $ |
| $200 - $399| 93                 | $ \frac{200 + 399}{2} = 299.5 $ |
| $400 - $599| 57                 | $ \frac{400 + 599}{2} = 499.5 $ |
| $600 - $799| 16                 | $ \frac{600 + 799}{2} = 699.5 $ |
| $800 - $999| 10                 | $ \frac{800 + 999}{2} = 899.5 $ |
| $1000 - $1199| 6                | $ \frac{1000 + 1199}{2} = 1099.5 $ |
| $1200 - $1399| 4                | $ \frac{1200 + 1399}{2} = 1299.5 $ |

Let me now compute the mean and standard deviation.The approximate mean amount of savings is **$229.97**. The standard deviation is **$227.35**.

Would you like more details or have any questions? Here are some related questions:

1. How does the standard deviation help in understanding the distribution of savings?
2. What is the significance of using midpoints in this calculation?
3. How would the mean and standard deviation change if one of the frequencies increased?
4. What are the implications of a low versus high standard deviation in financial data like savings?
5. How would the calculations differ if the intervals were not equal in width?

**Tip:** Understanding the standard deviation helps you grasp how spread out the savings amounts are around the mean, which is crucial for financial planning and analysis.

Recently, 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.

Learn how to calculate the approximate mean and standard deviation of savings amounts from survey data. This problem covers key statistical concepts such as midpoints, mean, and standard deviation, suitable for students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation