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The image shows a set of formulas and a question related to statistics, specifically dealing with the sample variance and sample standard deviation. Let's break them down step-by-step:

1. **First formula (sample variance formula):**
   \[
   \frac{n \sum(x^2) - \left( \sum x \right)^2}{n(n-1)} = \text{[first blank]}
   \]
   This is one way to compute the sample variance. It involves using the sum of squares of the individual data points and the sum of the data points themselves.

2. **Second formula (alternate form of sample variance):**
   \[
   \frac{\sum (x - \bar{x})^2}{n-1} = \text{[second blank]}
   \]
   This is the most common formula used to calculate the sample variance, where \( \bar{x} \) is the sample mean.

3. **Third (Sample standard deviation):**
   The question asks for the sample standard deviation \( s \), which is simply the square root of the sample variance.
   \[
   s = \sqrt{\text{sample variance}} = \text{[third blank]} \text{ (rounded to 4 decimal places)}
   \]

To proceed, you would need to plug in the values of the dataset to compute these quantities.

If you can provide the data points, I can help you fill in the blanks and calculate the sample variance and sample standard deviation. Let me know how you would like to proceed!

Here are 5 related questions that expand on this:

1. What is the relationship between population variance and sample variance?
2. How do you calculate the mean (\( \bar{x} \)) of a sample dataset?
3. What is the difference between sample variance and standard deviation?
4. Can you explain why we divide by \( n - 1 \) instead of \( n \) in sample variance?
5. How would the formulas change for a population instead of a sample?

**Tip:** Always verify that you are using the right formula for either population or sample data, as they slightly differ!

The image shows formulas related to statistics, specifically asking to calculate the sample variance and sample standard deviation.

Learn how to calculate sample variance and standard deviation using statistical formulas. This problem involves using the sum of squares and the mean to find the sample variance and standard deviation. Ideal for Grades 10-12.

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