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The question asks to calculate the standard deviation using the assumed mean method for the data set:

\[ 4, 11, 18, 25, 32 \]

### Steps to calculate Standard Deviation by the Assumed Mean Method:

1. **Choose an Assumed Mean (\(A\))**: Generally, you select a value from the data set. Let's choose \( A = 18 \) (the middle value of the data).

2. **Calculate the deviations (\(d_i = x_i - A\))** for each data point (\(x_i\)).

3. **Find \(d_i^2\)** (the square of the deviations).

4. **Calculate the sum of the deviations (\(\sum d_i\))** and the sum of squares of the deviations (\(\sum d_i^2\)).

5. **Use the formula** for the variance \( \sigma^2 \) and standard deviation \( \sigma \):

\[
\sigma^2 = \frac{\sum d_i^2}{n} - \left(\frac{\sum d_i}{n}\right)^2
\]
\[
\sigma = \sqrt{\sigma^2}
\]

Let me compute the values for you.The standard deviation of the given data set \([4, 11, 18, 25, 32]\) using the assumed mean method is approximately \(9.90\).

Would you like more details on any step of the process? 

Here are five related questions to expand your understanding:
1. How would the result change if we chose a different assumed mean?
2. What is the significance of choosing the assumed mean in this method?
3. How does standard deviation help in understanding data dispersion?
4. Can the assumed mean method be applied to grouped data?
5. How do variance and standard deviation differ conceptually?

**Tip**: When calculating standard deviation manually, using the assumed mean simplifies calculations, especially for larger datasets.

Calculate standard deviation by the Assumed Mean method for the data set 4, 11, 18, 25, 32.

Learn how to calculate standard deviation using the Assumed Mean method for the data set 4, 11, 18, 25, 32. This problem involves basic statistical concepts like variance and deviation and is suitable for students in Grades 9-12.

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