Find the SD of the given data set - 7, 2, 8, 11, 6, 13, 16 

To calculate the standard deviation (SD) of a given data set, follow these steps:

### Data Set:  
7, 2, 8, 11, 6, 13, 16

### Step 1: Find the Mean (Average)
The formula for the mean \( \mu \) is:

\[
\mu = \frac{\sum x_i}{n}
\]

where \( x_i \) represents each value in the data set, and \( n \) is the number of data points.

\[
\mu = \frac{7 + 2 + 8 + 11 + 6 + 13 + 16}{7} = \frac{63}{7} = 9
\]

### Step 2: Find the Squared Differences from the Mean
For each data point, subtract the mean and then square the result.

\[
(7 - 9)^2 = (-2)^2 = 4
\]
\[
(2 - 9)^2 = (-7)^2 = 49
\]
\[
(8 - 9)^2 = (-1)^2 = 1
\]
\[
(11 - 9)^2 = (2)^2 = 4
\]
\[
(6 - 9)^2 = (-3)^2 = 9
\]
\[
(13 - 9)^2 = (4)^2 = 16
\]
\[
(16 - 9)^2 = (7)^2 = 49
\]

### Step 3: Find the Variance
The variance \( \sigma^2 \) is the average of these squared differences. The formula for variance is:

\[
\sigma^2 = \frac{\sum (x_i - \mu)^2}{n}
\]

\[
\sigma^2 = \frac{4 + 49 + 1 + 4 + 9 + 16 + 49}{7} = \frac{132}{7} \approx 18.86
\]

### Step 4: Find the Standard Deviation
The standard deviation \( \sigma \) is the square root of the variance:

\[
\sigma = \sqrt{18.86} \approx 4.34
\]

### Conclusion:
The standard deviation of the data set is approximately **4.34**.

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Do you want more details or have any questions about the process?

Here are 5 related questions:
1. How does the standard deviation change if the dataset values increase by 5 each?
2. What is the variance of the data set?
3. How do outliers in a data set affect the standard deviation?
4. Can you explain the difference between sample standard deviation and population standard deviation?
5. How would removing the largest number from the data set affect the standard deviation?

**Tip:** Standard deviation provides insight into how much data points deviate from the mean, with a larger SD indicating more spread in the data.

Find the SD of the given data set - 7, 2, 8, 11, 6, 13, 16

Discover how to calculate the standard deviation of the data set 7, 2, 8, 11, 6, 13, 16 with a step-by-step guide. Learn the concepts of mean, variance, and standard deviation. Suitable for high school students in Grades 9-12.

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