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Part 1
Find the standard deviation for the group of data items.
9, 5​, 9, 5​, 9​, 5, 9​, 5
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Part 1
The standard deviation is enter your response here.

To find the standard deviation for the given group of data items:

The data set is:  
\( 9, 5, 9, 5, 9, 5, 9, 5 \)

### Steps:
1. **Find the mean** (average) of the dataTo find the standard deviation for the given group of data items:

The data set is:  
\( 9, 5, 9, 5, 9, 5, 9, 5 \)

### Steps:
1. **Find the mean** (average) of the 
   \[
   \text{Mean} = \frac{9 + 5 + 9 + 5 + 9 + 5 + 9 + 5}{8} = \frac{56}{8} = 7
   \]

2. **Calculate the squared deviations** from the mean for each data point:
   \[
   (9 - 7)^2 = 4, \quad (5 - 7)^2 = 4
   \]
   Repeating for all values, we get:
   \[
   4, 4, 4, 4, 4, 4, 4, 4
   \]

3. **Find the average of these squared deviations** (variance):
   \[
   \text{Variance} = \frac{4 + 4 + 4 + 4 + 4 + 4 + 4 + 4}{8} = \frac{32}{8} = 4
   \]

4. **Take the square root** of the variance to find the standard deviation:
   \[
   \text{Standard deviation} = \sqrt{4} = 2
   \]

Thus, the standard deviation is **2**.

---

Would you like more details on any step? Here are some related questions:

1. How do we interpret the standard deviation in this context?
2. What happens to the standard deviation if we change one of the 9s to a different number?
3. How does standard deviation differ from variance in concept?
4. Why do we use the square of deviations when calculating variance?
5. What is the standard deviation formula for a sample versus a population?

**Tip**: Standard deviation measures how spread out the data is relative to the mean.

Find the standard deviation for the group of data items. 9, 5, 9, 5, 9, 5, 9, 5.

Learn how to calculate the standard deviation for the data set 9, 5, 9, 5, 9, 5, 9, 5. This step-by-step guide covers key statistical concepts such as mean, variance, and standard deviation, making it ideal for students in Grades 8-10.

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