It seems you included an "e" in the data set, which is likely a typo. Let's correct it and proceed with the numbers. Based on your input, the correct data set should be:

7, 6, 4, 5, 5, 2, 1, 2

Now, let's calculate the mean, range, and standard deviation (SD).

1. Mean (Average)

$\text{Mean} = \frac{\sum \text{(all numbers)}}{\text{number of values}}$ $\text{Mean} = \frac{7 + 6 + 4 + 5 + 5 + 2 + 1 + 2}{8} = \frac{32}{8} = 4$

2. Range

$\text{Range} = \text{Max value} - \text{Min value}$ $\text{Range} = 7 - 1 = 6$

3. Standard Deviation (SD)

The formula for standard deviation is: $\text{SD} = \sqrt{\frac{\sum (x_i - \mu)^2}{n}}$ Where $\mu$ is the mean, and $x_i$ are the values.

Let's compute this.

Here are the results:

• Mean: 4.0
• Range: 6
• Standard Deviation (SD): 2.0

Do you want more details or have any questions?

Here are five related questions to expand your understanding:

1. How does standard deviation help measure data dispersion?
2. What would happen if you added an outlier to the data set?
3. How is the range different from standard deviation in interpreting variability?
4. What is the variance, and how is it related to the standard deviation?
5. How do the mean and median compare when the data set is skewed?

Tip: The standard deviation is more sensitive to outliers than the mean!