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This is exercise $35$ of page $34$ of Probability and Statistics by J. Devore.

A sample of observations is given: $15,13,18.0,14.5, 12.0,11,8.9$ and $8.0$.

Then the question is:

By how much could the smallest value (in this case $8$) be increased without affecting the value of the sample median?

The median is clearly 12.5.

So my answer is: to any number less or equal than 12. However, the book says that "any number smaller than 12". But couldn't it be 12 as well?

Also in this case, which is a better indicator? mean or median? both are almost the same, so which one do you tend to choose?

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It certainly seems to me that it could be $12$ also, provided median is construed as the central value when there are an odd number of elements, and the average of the two central values where there are an even number of elements. Is that how the median is defined in the book?


Without a specific objective, you can't say in this case which is a better indicator of central tendency: mean or median. In general, however, median is a robust indicator of central tendency, whereas mean isn't. See robust statistics for more details.

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