x
29.2
9.1
15.6
23.4
4.5
17.2
26.6


Standard deviation:

To calculate the standard deviation of the given data set, we will follow these steps:

### Data set:
- \( 29.2, 9.1, 15.6, 23.4, 4.5, 17.2, 26.6 \)

### Steps:
1. **Find the mean (average)**:
   \[
   \text{Mean} = \frac{\sum x}{n}
   \]
   where \( n \) is the number of data points.

2. **Calculate the squared differences from the mean** for each value.

3. **Find the variance**:
   \[
   \text{Variance} = \frac{\sum (\text{value} - \text{mean})^2}{n}
   \]

4. **Calculate the standard deviation**:
   \[
   \text{Standard Deviation} = \sqrt{\text{Variance}}
   \]

Let me calculate that for you.The standard deviation of the given data set is approximately \( 8.42 \).

Would you like further details on how this was calculated or any related clarifications?

Here are 5 questions related to this concept:
1. What is the difference between population and sample standard deviation?
2. How does the standard deviation relate to data spread or variability?
3. How does removing or adding a data point affect the standard deviation?
4. Can you explain the concept of variance in relation to standard deviation?
5. How does standard deviation differ from the mean absolute deviation?

**Tip:** A smaller standard deviation indicates that the data points are close to the mean, while a larger one indicates more spread out data.

Calculate the standard deviation of the data set: 29.2, 9.1, 15.6, 23.4, 4.5, 17.2, 26.6

Learn how to calculate the standard deviation of the data set: 29.2, 9.1, 15.6, 23.4, 4.5, 17.2, 26.6. This problem explores essential concepts in statistics, including mean, variance, and standard deviation. Suitable for students in Grades 9-12.

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