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Chapter 6: Q20 (page 265)

Mean Absolute DeviationIs the mean absolute deviation of a sample a good statistic for estimating the mean absolute deviation of the population? Why or why not?

Short Answer

Expert verified

No, the mean absolute deviation of a sample is not a good statistic for estimating the mean absolute deviation of the population because it is a biased estimator.

Step by step solution

01

Given information

The sample mean absolute deviation is considered a good statistic for estimating the population’s mean absolute deviation.

02

Good statistic

A good statistic for estimating a population parameter is the one that is an unbiased estimator of the population parameter.

That is, if the mean of all the values of the sample statistic (for a large number of samples) is equal to the population parameter, it is considered a good statistic.

The mean absolute deviation of a sample is a biased estimator of the mean absolute deviation of the population.

Therefore mean absolute deviation of a sample is not a good statistic for the estimation of the mean absolution deviation of the population.

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