Use the values Σ*x*i=56.80   mm2Σ*x*i2= 197.9146  mm4
 to compute the sample variance *s*2 and then the sample standard deviation *s*. (Round your answers to four decimal places.)

To compute the sample variance \( s^2 \) and the sample standard deviation \( s \), we use the following formulas:

1. **Sample variance formula**:
\[
s^2 = \frac{1}{n-1} \left( \sum{x_i^2} - \frac{(\sum{x_i})^2}{n} \right)
\]
where:
- \( \sum{x_i} \) is the sum of the data points.
- \( \sum{x_i^2} \) is the sum of the squares of the data points.
- \( n \) is the number of data points in the sample.

2. **Sample standard deviation formula**:
\[
s = \sqrt{s^2}
\]

### Given values:
- \( \sum{x_i} = 56.80 \, \text{mm}^2 \)
- \( \sum{x_i^2} = 197.9146 \, \text{mm}^4 \)

Let's denote the number of data points as \( n \), but it's not provided directly. We can solve for \( n \) using these values. Let me calculate both \( s^2 \) and \( s \).It appears the sample variance calculation resulted in a negative value, which is not physically meaningful, and the standard deviation returned a complex number. This suggests that either the number of data points \( n \) assumed is incorrect or additional context for the problem is missing.

To ensure a correct solution, I need clarification on the number of data points \( n \). Could you provide the value of \( n \) or confirm if there’s another interpretation for the given data?

Feel free to share more details, and I’ll recalculate the values.

Use the values Σ*x*i=56.80 mm² Σ*x*i²=197.9146 mm⁴ to compute the sample variance *s²* and then the sample standard deviation *s*. (Round your answers to four decimal places.)

Learn how to calculate the sample variance and standard deviation using the values Σx = 56.80 mm² and Σx² = 197.9146 mm⁴. This problem involves key statistical concepts, including the formulas for variance and standard deviation. Suitable for students in Grades 10-12.

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