Question

Let a population consist of the values 10 cigarettes, 21cigarettes, and 22

cigarettes smoked in a day. Show that when samples of size 2 are randomly selected with replacement, the samples have mean absolute deviations that do not center about the value of the mean absolute deviation of the population. What does this indicate about a sample mean absolute deviation is used as an estimator of the mean absolute deviation of a population?

Calculate the mean absolute deviation for each possible sample of size 2 from the population.

Sample	Mean Absolute Deviation
{10 ,10 }
{10 ,21 }
{10 ,22 }
{21,10 }
{21,21 }
{21 ,22 }
{22 ,10 }
{22 ,21 }
{22 ,22 }

(Type integers or decimals rounded to one decimal place as needed.)

Answer 1

	mean absolute deviation
10,10	0
10,21	5.5
10,22	6
21,10	5.5
21,21	0
21,22	0.5
22,10	6
22,21	0.5
22,22	0

value of the mean absolute deviation of the population =5.11

and mean absolute deviation of the sample =2.67