Seth asked a random sample of 20 students how much cash they had in their pocket. The following frequency table gives the responses.
cash($) freq
0.        1
1.        2
5.       4
20.     11
44.     1
985.   1
Find the standard deviation. Give your answer to at least 2 decimal places

To calculate the standard deviation of a frequency distribution, we use the formula:

\[
\sigma = \sqrt{\frac{\sum{f(x - \mu)^2}}{N}}
\]

Where:
- $x$ = the cash amount (given in the table)
- $f$ = frequency (number of students)
- $N$ = total number of students
- $\mu$ = mean of the distribution

Let's follow these steps:

1. **Find the mean $\mu$**:
   \[
   \mu = \frac{\sum{f \cdot x}}{N}
   \]

2. **Use the mean to calculate the variance**:
   \[
   \text{Variance} = \frac{\sum{f(x - \mu)^2}}{N}
   \]

3. **Standard deviation** is the square root of the variance.

I'll now compute this.The standard deviation of the cash amounts is approximately $ 211.65 $.

Would you like further details or have any questions about the process?

Here are 5 related questions to expand on this concept:
1. How would the standard deviation change if the extreme outlier (\$985) was removed?
2. Can you explain why the mean and standard deviation are sensitive to outliers?
3. What would happen to the standard deviation if all the cash amounts were doubled?
4. How is standard deviation different from variance, and why is it often preferred?
5. Could you compare this standard deviation with that of a larger sample?

**Tip:** When calculating the standard deviation, extreme outliers can significantly affect the result, so always check the data for such values!

Seth asked a random sample of 20 students how much cash they had in their pocket. The following frequency table gives the responses.
cash($) freq
0. 1
1. 2
5. 4
20. 11
44. 1
985. 1
Find the standard deviation. Give your answer to at least 2 decimal places.

Learn how to calculate the standard deviation of a frequency distribution. Seth's sample of 20 students' cash amounts includes values like $0, $5, and even an outlier of $985. Follow the step-by-step solution to find the standard deviation to two decimal places. Suitable for students in Grades 9-12.

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