Content attribution QUESTION 18 - 1 POINT The following data set represents the ages of all six grandchildren in a family. Find the variance for this data set of ages: $6,3,14,11,14,6$ - Round the final answer to one decimal place. Provide your answer below:
Solution
Step 1 ：The given data set of ages is: \(6, 3, 14, 11, 14, 6\).
Step 2 ：The variance of a data set is a measure of how much values in the set vary on average with respect to the mean. The formula for variance is: \(\sigma^2 = \frac{\sum_{i=1}^{n} (x_i - \mu)^2}{n}\) where \(x_i\) is each value in the set, \(\mu\) is the mean of the set, and \(n\) is the number of values in the set.
Step 3 ：First, we need to calculate the mean of the data set. The mean age is \(9.0\).
Step 4 ：Then, we subtract the mean from each value in the set, square the result, and sum all these squared results.
Step 5 ：Finally, we divide this sum by the number of values in the set. The variance is \(18.0\).
Step 6 ：Final Answer: The variance for this data set of ages is \(\boxed{18.0}\).
