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?