Ages (Example 6) A father has five children of ages 2, 3, 5, 8, and 9 years.

a. Calculate the standard deviation of their current ages.

b. Without doing any calculation, indicate whether the standard deviation of the children's ages in the next 15 years will be larger, smaller, or the same as the standard deviation of their current ages. Check your answers by calculating the standard deviation of the ages in 15 years. Explain how adding 15 to each number affects the standard deviation.

c. Find the mean of the children at their current ages.

d. Without doing any calculation, indicate whether the mean of the children's age in the next 15 years will be larger, smaller, or the same as the mean of the current ages. Confirm your answer, and describe how adding 15 to each number affects the mean.