https://file.aiquickdraw.com/mathbot/file/1726595552097abwstnqz.jpg

The image provides a frequency distribution of the number of pairs of shoes owned by 58 students. We need to calculate the mean and the sample standard deviation based on the provided data.

Here's how to approach the problem:

1. **Mean** (\( \bar{x} \)):
   \[
   \bar{x} = \frac{\sum (x_i \cdot f_i)}{n}
   \]
   where \(x_i\) is the number of pairs of shoes, \(f_i\) is the frequency, and \(n\) is the total number of students (58).

2. **Sample Standard Deviation** (\( s \)):
   \[
   s = \sqrt{\frac{\sum (f_i \cdot (x_i - \bar{x})^2)}{n - 1}}
   \]
   Let's calculate these values now.The calculations yield the following results:

- The mean number of pairs of shoes (\( \bar{x} \)) is approximately \( 7.0517 \).
- The sample standard deviation (\( s \)) is approximately \( 2.0978 \).

Do you need further details or have any questions?

Here are five related questions for further exploration:
1. How does the sample size affect the standard deviation?
2. What is the difference between population and sample standard deviation?
3. How can this frequency distribution be visualized graphically?
4. How would the mean change if the largest number of pairs of shoes increased?
5. Why is it important to round to 4 decimal places in statistics?

**Tip:** Remember that sample standard deviation is typically used when dealing with a sample of a population, not the entire population itself.

A random sample of 58 students was selected, and they were asked the number of pairs of shoes they have. The results are shown in a frequency distribution. Calculate the mean (\(\bar{x}\)) and the sample standard deviation (\(s\)) rounded to 4 decimal places.

Calculate the mean and sample standard deviation for a frequency distribution of the number of pairs of shoes owned by 58 students. This problem covers key statistical concepts, including calculating the mean and sample standard deviation from a frequency table. Suitable for students in Grades 10-12.

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