https://file.aiquickdraw.com/mathbot/file/1726321034828iom0v4jq.jpg

The image shows a frequency distribution table with class intervals, frequencies, and the given approximations for the sample mean \(\bar{x}\) and the sample standard deviation \(s\). Let’s go step by step:

### Frequency Distribution Table:

| Class   | Frequency (f) |
|---------|---------------|
| 0-4     | 5             |
| 5-9     | 12            |
| 10-14   | 19            |
| 15-19   | 16            |
| 20-24   | 15            |
| 25-29   | 9             |
| 30+     | 7             |

### Given Approximations:
- Sample Mean: \(\bar{x} = 16.8\)
- Sample Standard Deviation: \(s = 8.3\)

To calculate these, we follow these steps:

1. **Midpoints (Class Marks)**: Calculate the midpoints of each class.
2. **Mean Formula**: \[
\bar{x} = \frac{\sum (f \cdot x)}{\sum f}
\]
where \(x\) is the class midpoint.
3. **Standard Deviation Formula**: \[
s = \sqrt{\frac{\sum f(x - \bar{x})^2}{\sum f - 1}}
\]
where \(\bar{x}\) is the mean.

Would you like me to calculate the values for the mean and standard deviation step by step or provide further explanation on a specific part?

### Relative Questions:
1. How are class midpoints calculated?
2. How does changing the frequency affect the mean?
3. What is the impact of outliers in a frequency distribution?
4. How do we interpret the sample standard deviation in this context?
5. Can you explain the difference between population and sample standard deviation?

### Tip:
Always ensure that the class intervals are consistent when constructing a frequency distribution. This allows for accurate calculation of central tendencies.

Construct the frequency distribution and find approximations for the sample mean and sample standard deviation based on the given data.

Learn how to construct a frequency distribution and find approximations for the sample mean (x̄ = 16.8) and sample standard deviation (s = 8.3). This problem involves calculating the mean and standard deviation using class midpoints and frequency data. Suitable for students in Grades 10-12 or introductory college statistics.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation