There are three children in a room, ages 3, 4, and 5. If another 4-year-old enters the room:
A)the mean age will stay the same, but the variance will increase.
B)the mean age will stay the same, but the variance will decrease.
C)the mean age and variance will stay the same.
D)the mean age and variance will increase.

Question

Quizplus · Accepted Answer

Initially, the mean age is (3+4+5)/3 = 4. Adding another 4-year-old does not change the mean (3+4+5+4)/4 = 4. However, adding a value equal to the mean decreases the variance because it reduces the spread of the ages around the mean.

There Are Three Children in a Room, Ages 3, 4