https://file.aiquickdraw.com/mathbot/file/1726435600346jlehqtq4.jpg

From the image, it looks like you're working on a statistical formula that resembles a variance calculation. The formula you're using sums up the squared deviations from the mean, then divides by \( n - 1 \), which suggests it's likely the sample variance formula.

The formula can be written as:
\[
S^2 = \frac{ \sum (x_i - \bar{x})^2 }{n - 1}
\]
where:
- \( x_i \) represents each data point,
- \( \bar{x} \) is the mean of the data,
- \( n \) is the number of data points.

In the numerator, you're calculating the squared difference between each data point and the mean (which appears to be 155.42) and summing those values. The denominator, \( 12 - 1 = 11 \), corresponds to the degrees of freedom for the sample (since you have 12 data points).

Let me know if you'd like to compute the variance or if you need a detailed step-by-step solution.

Would you like more details or any clarification?

Here are 5 related questions:
1. How is sample variance different from population variance?
2. How is standard deviation related to variance?
3. Why is it important to divide by \(n-1\) instead of \(n\) in sample variance?
4. Can you explain what "degrees of freedom" means in the context of variance calculation?
5. What is the significance of using squared differences in variance calculations?

**Tip**: After calculating variance, taking the square root gives you the standard deviation, which is often more interpretable as it’s in the same units as the data points.

Calculate the sample variance using the data points: 100, 105, 110, 130, 135, 138, 142, 145, 150, 170, 240, 300 with a mean of 155.42.

Learn how to calculate the sample variance for a data set using the formula for variance, where each data point’s deviation from the mean (155.42) is squared and summed. The data includes values like 100, 105, 110, and 300. This detailed explanation helps in understanding variance and the role of degrees of freedom in statistics.

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