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According to my Professor, the answer to this question is the MEDIAN. However, wouldn't MODE be a better measure of central tendency? The mode is almost never affected by extreme outliers..please help explain this. THANKS

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    $\begingroup$ Mode is often not informative. Think for example of a nearly uniform distribution with a few wild entries. $\endgroup$ Feb 1, 2014 at 1:53
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    $\begingroup$ There is a big difference between distributions with long tails, such as density $\frac{2}{\pi}\frac{1}{1+x^2}$, for $x\ge 0$, and the exponential. Each has mode $0$. Mode is often a pretty bad measure of central tendency. $\endgroup$ Feb 1, 2014 at 2:39

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No. The mode is very sensitive to the observed frequencies. For example, the data

$$\{ 1, 1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 7, 10, 100 \}$$

has a mode of 1, but the similar shaped distribution

$$\{ 1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 7, 10, 100 \}$$

has a mode of 4.

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If your sample consists of 1000 distinct points in $[0,1]$ and two more samples equal to $100$, I would say $100$ is the outlier, but it is also the mode. The mode in this case is clearly NOT a good measure of central tendency, right?

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