Find the standard deviation for 2
,
17
,
12
,
5
,
7
,
10
,
5
,
8
,
6

To calculate the standard deviation for the data set \( 2, 17, 12, 5, 7, 10, 5, 8, 6 \), follow these steps:

### 1. Find the mean:
The mean \( \mu \) is the sum of all numbers divided by the number of data points.

\[
\mu = \frac{2 + 17 + 12 + 5 + 7 + 10 + 5 + 8 + 6}{9}
\]

\[
\mu = \frac{72}{9} = 8
\]

### 2. Find the squared differences from the mean:
For each number in the data set, subtract the mean and square the result.

\[
(2 - 8)^2 = (-6)^2 = 36
\]
\[
(17 - 8)^2 = (9)^2 = 81
\]
\[
(12 - 8)^2 = (4)^2 = 16
\]
\[
(5 - 8)^2 = (-3)^2 = 9
\]
\[
(7 - 8)^2 = (-1)^2 = 1
\]
\[
(10 - 8)^2 = (2)^2 = 4
\]
\[
(5 - 8)^2 = (-3)^2 = 9
\]
\[
(8 - 8)^2 = (0)^2 = 0
\]
\[
(6 - 8)^2 = (-2)^2 = 4
\]

### 3. Find the average of the squared differences:
\[
\text{Variance} = \frac{36 + 81 + 16 + 9 + 1 + 4 + 9 + 0 + 4}{9}
\]
\[
\text{Variance} = \frac{160}{9} \approx 17.78
\]

### 4. Take the square root of the variance to find the standard deviation:
\[
\sigma = \sqrt{17.78} \approx 4.21
\]

### Conclusion:
The standard deviation is approximately \( 4.21 \).

Do you need further details or have any questions?

Here are 5 related questions:
1. What is the difference between standard deviation and variance?
2. How does changing a single value affect the standard deviation?
3. What is the significance of a low standard deviation versus a high one?
4. How would you calculate the standard deviation of a larger dataset?
5. Can you calculate standard deviation using other measures of central tendency?

**Tip:** Standard deviation gives a measure of how spread out the numbers in your data set are from the mean.

Find the standard deviation for 2, 17, 12, 5, 7, 10, 5, 8, 6

Learn how to calculate the standard deviation for the data set 2, 17, 12, 5, 7, 10, 5, 8, 6. This problem covers key statistical concepts like mean, variance, and standard deviation with a step-by-step solution. Suitable for students in Grades 9-12.

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