Calculate the population variance, population standard deviation, sample variance, and sample standard deviation for the following data:
10    -10    -9    4    -5    -1    -2    -4    -8
Calculate your answer using a Spreadsheet template.

I'll guide you on how to calculate the population variance, population standard deviation, sample variance, and sample standard deviation using a spreadsheet. The following steps outline the process:

### Steps to Create the Spreadsheet Template:

1. **Enter the Data**:
   - In the first column (Column A), list your data values from cell A1 to A9:
     ```
     10
     -10
     -9
     4
     -5
     -1
     -2
     -4
     -8
     ```

2. **Population Variance**:
   - In cell B1, you can enter the formula for population variance:
     ```
     =VAR.P(A1:A9)
     ```
   - This calculates the variance considering the entire dataset as the population.

3. **Population Standard Deviation**:
   - In cell B2, enter the formula for population standard deviation:
     ```
     =STDEV.P(A1:A9)
     ```
   - This returns the population standard deviation.

4. **Sample Variance**:
   - In cell B3, input the formula for sample variance:
     ```
     =VAR.S(A1:A9)
     ```
   - This calculates the sample variance, which is useful when the data represents a sample of a larger population.

5. **Sample Standard Deviation**:
   - In cell B4, type the formula for sample standard deviation:
     ```
     =STDEV.S(A1:A9)
     ```
   - This provides the sample standard deviation.

### Explanation:

- **Population Variance** (\( \sigma^2 \)): Measures how much the data points spread out from the mean for the entire population.
- **Population Standard Deviation** (\( \sigma \)): The square root of the population variance, showing the average distance of the data points from the mean.
- **Sample Variance** (\( s^2 \)): Similar to population variance, but adjusted to account for the sample size (using \( n - 1 \) instead of \( n \)).
- **Sample Standard Deviation** (\( s \)): The square root of the sample variance.

### Do you want further details or have any questions?

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Here are 5 related questions:

1. What’s the difference between sample and population variance?
2. How do changes in the dataset affect standard deviation?
3. What are the implications of higher variance in a dataset?
4. How is standard deviation used in real-world scenarios?
5. What are the advantages of using spreadsheets for statistical analysis?

**Tip**: When using large datasets, spreadsheets' built-in functions make calculations faster and less prone to error.

Calculate the population variance, population standard deviation, sample variance, and sample standard deviation for the following data

Learn how to calculate the population variance, population standard deviation, sample variance, and sample standard deviation for the data set 10, -10, -9, 4, -5, -1, -2, -4, -8 using spreadsheet formulas. This guide provides step-by-step instructions and formulas for students in Grades 10-12.

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