Question

Let a population consist of the values ​cigarettes, ​cigarettes, and 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?.

Answer 1

The "sample" with "mean absolute deviation" indicate about a sample mean absolute deviation is being used as an estimator of the mean absolute deviation of a​ population

• Mean of the sample MAD=3.3
• Population MAD =6.4

What does this indicate about a sample mean absolute deviation used as an estimator of the mean absolute deviation of a​ population?

Generally,  The MAD measures the average dispersion around the mean of a given data collection.

$1/n \sum_i-1^{n} |x_i -m(X)|$

In conclusion, for the corresponding same to mean

the sample  mean absolute deviation

7,7  ↔         0

7,21  ↔         7

7,22         ↔    7.5

21,7        ↔          7

21,21 ↔     0

21,22 ↔    0.5

22,7   ↔     7.5

Therefore

• Mean of the sample MAD=3.3
• Population MAD =6.4

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