Questions: Find the range and standard deviation of the set of data. 12,8,7,11,17 The range is 10. (Simplify your answer.) The standard deviation is (Round to the nearest hundredth as needed.)

Solution Steps

The range of a dataset is calculated as the difference between the maximum and minimum values. For the given data set \( \{12, 8, 7, 11, 17\} \):

\[ \text{Range} = \max(x_i) - \min(x_i) = 17 - 7 = 10 \]

The mean \( \mu \) of the dataset is calculated using the formula:

\[ \mu = \frac{\sum x_i}{n} = \frac{12 + 8 + 7 + 11 + 17}{5} = \frac{55}{5} = 11.0 \]

The variance \( \sigma^2 \) is calculated using the formula:

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

Calculating each term:

• \( (12 - 11)^2 = 1 \)
• \( (8 - 11)^2 = 9 \)
• \( (7 - 11)^2 = 16 \)
• \( (11 - 11)^2 = 0 \)
• \( (17 - 11)^2 = 36 \)

Summing these values:

\[ \sum (x_i - \mu)^2 = 1 + 9 + 16 + 0 + 36 = 62 \]

Thus, the variance is:

\[ \sigma^2 = \frac{62}{5} = 12.4 \]

The standard deviation \( \sigma \) is the square root of the variance:

\[ \sigma = \sqrt{12.4} \approx 3.52 \]

Final Answer