Integer Sample
Source:
February 21, 2006
floor functionabsolute value
Problem Statement
A sample of 121 integers is given, each between 1 and 1000 inclusive, with repetitions allowed. The sample has a unique mode (most frequent value). Let be the difference between the mode and the arithmetic mean of the sample. What is the largest possible value of ? (For real , is the greatest integer less than or equal to .)