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

Given data set: 7, 2, 8, 11, 6, 13, 16

Step 1: Find the mean (average)

$\text{Mean} = \frac{7 + 2 + 8 + 11 + 6 + 13 + 16}{7} = \frac{63}{7} = 9$

Step 2: Calculate each data point's deviation from the mean and square it

• (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 average of these squared differences (Variance)

$\text{Variance} = \frac{4 + 49 + 1 + 4 + 9 + 16 + 49}{7} = \frac{132}{7} \approx 18.86$

Step 4: Take the square root of the variance to find the standard deviation

$\text{Standard Deviation} = \sqrt{18.86} \approx 4.34$

So, the standard deviation of the given data set is approximately 4.34.

Would you like more details or have any questions?

Here are 5 related questions you might find useful:

1. How do you interpret a standard deviation value?
2. What is the difference between population and sample standard deviation?
3. How does increasing the number of data points affect the standard deviation?
4. Can standard deviation ever be negative?
5. What is the relationship between standard deviation and variance?

Tip: The larger the standard deviation, the more spread out the data is from the mean.