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It looks like you've uploaded an image asking for the calculation of the standard deviation for the data set \(4, 11, 18, 25, 32\). Let's solve this in tabular format.

### Steps to calculate Standard Deviation:
1. **Find the mean (average)** of the numbers.
2. **Calculate each data point's deviation** from the mean.
3. **Square each deviation**.
4. **Find the average of these squared deviations** (this is the variance).
5. **Take the square root** of the variance to find the standard deviation.

#### Data set: \(4, 11, 18, 25, 32\)

Let's proceed to calculate the standard deviation using a table.

| \(x_i\) (Data) | \(x_i - \bar{x}\) (Deviation from Mean) | \((x_i - \bar{x})^2\) (Squared Deviation) |
|----------------|-----------------------------------------|-------------------------------------------|
| 4              |                                         |                                           |
| 11             |                                         |                                           |
| 18             |                                         |                                           |
| 25             |                                         |                                           |
| 32             |                                         |                                           |

I'll calculate each step and fill the table now.Here is the tabular breakdown for the standard deviation calculation of the data set \(4, 11, 18, 25, 32\):

| \(x_i\) (Data) | \(x_i - \bar{x}\) (Deviation from Mean) | \((x_i - \bar{x})^2\) (Squared Deviation) |
|----------------|-----------------------------------------|-------------------------------------------|
| 4              | -14                                     | 196                                       |
| 11             | -7                                      | 49                                        |
| 18             | 0                                       | 0                                         |
| 25             | 7                                       | 49                                        |
| 32             | 14                                      | 196                                       |

- **Mean**: \( \bar{x} = 18 \)
- **Variance**: \( 98 \)
- **Standard Deviation**: \( 9.90 \)

Would you like further explanation or have any questions about this?

Here are some questions to expand on:
1. What is the difference between population and sample standard deviation?
2. How does standard deviation differ from variance?
3. In what situations is it important to use standard deviation over other measures of spread?
4. Can the standard deviation ever be negative?
5. How does standard deviation behave with outliers?

**Tip:** Always check if you're calculating for a population or a sample, as formulas differ slightly!

Calculate standard deviation for the data set 4, 11, 18, 25, 32.

Learn how to calculate the standard deviation for the data set 4, 11, 18, 25, 32. This step-by-step solution involves finding the mean, calculating deviations from the mean, and determining the variance and standard deviation. Suitable for students in Grades 9-12.

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