Question

Let a population consist of the values 7 cigarettes,8 cigarettes, 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 being 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
​{7,7​}	nothing
​{7,8​}	nothing
​{7,22​}	nothing
​{8,7​}	nothing
​{8 ,8​}	nothing
​{8 ,22​}	nothing
​{22,7​}	nothing
​{22,8​}	nothing
​{22 ,22​}	nothing

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

Answer 1

	mean absolute deviation
7,7	0
7,8	0.5
7,22	7.5
8,7	0.5
8,8	0
8,22	7
22,7	7.5
22,8	7
22,22	0

mean absolute deviation of the population =6.44 which is not equal to mean of sampling distribution of mean absolute deviation 3.33

therefore it is not an unbiased estimator of population mean absolute deviation