6, 6, 6, 9, 12, 12, 12   find the sample standard deviation 

To calculate the sample standard deviation, follow these steps:

### 1. Find the mean (\(\bar{x}\)) of the data set:
The data set is: \( 6, 6, 6, 9, 12, 12, 12 \).

\[
\bar{x} = \frac{\text{sum of all data points}}{\text{number of data points}} = \frac{6 + 6 + 6 + 9 + 12 + 12 + 12}{7} = \frac{63}{7} = 9
\]

### 2. Calculate each data point's deviation from the mean and square it:
- \( (6 - 9)^2 = (-3)^2 = 9 \)
- \( (6 - 9)^2 = (-3)^2 = 9 \)
- \( (6 - 9)^2 = (-3)^2 = 9 \)
- \( (9 - 9)^2 = (0)^2 = 0 \)
- \( (12 - 9)^2 = (3)^2 = 9 \)
- \( (12 - 9)^2 = (3)^2 = 9 \)
- \( (12 - 9)^2 = (3)^2 = 9 \)

### 3. Find the sum of these squared deviations:
\[
9 + 9 + 9 + 0 + 9 + 9 + 9 = 54
\]

### 4. Divide by the number of data points minus 1 (since this is a sample):
\[
\frac{54}{7-1} = \frac{54}{6} = 9
\]

### 5. Take the square root of the result to get the sample standard deviation:
\[
\sqrt{9} = 3
\]

### The sample standard deviation is **3**.

Would you like more details or have any questions?

Here are 5 related questions:
1. How would you compute the population standard deviation?
2. What is the variance, and how does it relate to standard deviation?
3. Can you explain the difference between sample and population data?
4. How does increasing the sample size affect the standard deviation?
5. What are the properties of a normal distribution in terms of standard deviation?

**Tip:** Always check whether the data represents a sample or the entire population before choosing the formula.

6, 6, 6, 9, 12, 12, 12   find the sample standard deviation

Learn how to calculate the sample standard deviation for the data set 6, 6, 6, 9, 12, 12, 12 with a detailed step-by-step solution. This problem involves calculating the mean, variance, and sample standard deviation, and is suitable for students in Grades 9-12.

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