Questions: Part 1 of 3 Find the range. The range is 30 . Part 2 of 3 Find the variance. The variance is 90 . Part 3 of 3 Find the standard deviation. The standard deviation is .

Solution Steps

The range of a dataset is calculated as:

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

For the given dataset, the maximum value is \(100\) and the minimum value is \(10\):

\[ \text{Range} = 100 - 10 = 90 \]

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

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

Where \( n \) is the number of data points. For the dataset, we have:

\[ \mu = \frac{550}{10} = 55.0 \]

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

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

Substituting the values, we find:

\[ \sigma^2 = 825.0 \]

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

\[ \sigma = \sqrt{825.0} \approx 28.7 \]

Final Answer