Mrs. Johnson’s children are 2, 2, 3, and 5 years of age.

a. Calculate the standard deviation of their current ages.

b. Without doing any calculation, indicate whether the standard deviation of the ages in 20 years will be larger, smaller, or the same as the standard deviation of their current ages. Check your answer by calculating the standard deviation of the ages in 20 years. Explain how adding 20 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 age in 20 years will be larger, smaller, or about the same as the mean of the current ages. Confirm your answer, and describe how adding 20 to each number affects the mean.