Compute the sample variance and sample standard deviation (to 2 decimals).

To compute the **sample variance** and **sample standard deviation**, we'll need a dataset. If you provide a list of numbers, I can calculate them for you.

Here’s the general approach:

### Steps to Compute Sample Variance (\( s^2 \)):
1. **Find the mean** \( \bar{x} \) of the sample dataTo compute the **sample variance** and **sample standard deviation**, we'll need a dataset. If you provide a list of numbers, I can calculate them for you.

Here’s the general approach:

### Steps to Compute Sample Variance (\( s^2 \)):
1. **Find the mean** \( \bar{x} \) of the sample 
   \[
   \bar{x} = \frac{\sum x_i}{n}
   \]
   where \( x_i \) represents each value in the dataset and \( n \) is the sample size.

2. **Subtract the mean** from each data point and square the result (these are the squared deviations from the mean):
   \[
   (x_i - \bar{x})^2
   \]

3. **Sum up** all the squared deviations:
   \[
   \sum (x_i - \bar{x})^2
   \]

4. **Divide by** \( n - 1 \) (degrees of freedom):
   \[
   s^2 = \frac{\sum (x_i - \bar{x})^2}{n - 1}
   \]
   This gives the sample variance.

### Steps to Compute Sample Standard Deviation (\( s \)):
1. Take the square root of the sample variance:
   \[
   s = \sqrt{s^2}
   \]

Once you provide the data, I can carry out the calculations and give the results to 2 decimal places.

Do you have any questions or details you'd like to add? Here are some related questions you might find helpful:
1. What’s the difference between sample variance and population variance?
2. How do degrees of freedom affect the sample variance?
3. Can variance be negative, and why or why not?
4. What are some real-world applications of variance and standard deviation?
5. What’s the relationship between standard deviation and normal distribution?

**Tip:** For small datasets, using the sample variance formula is important because it accounts for the potential variability that could be underestimated if using population variance formulas.

Compute the sample variance and sample standard deviation (to 2 decimals).

Learn how to calculate the sample variance and sample standard deviation step by step, using key statistical formulas. This guide explains the importance of degrees of freedom and the process for finding the sample mean, variance, and standard deviation, with examples. Ideal for Grades 10-12.

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