# Range of averages

Find these 4 numbers, given their mode, median and range.

## Problem

Find the 4 numbers which have a mode of 12, a median of 14 and a range of 10.

*This problem is taken from the World Mathematics Championships*

## Student Solutions

12 is the mode, so 12 must appear at least twice.

The median, 14, is half way between the two middle numbers when listed in order of size. So the 12s must be below the median, since the median is greater than 12.

__12__,

__12__,

__,__

14 is half way between 12 and 16, so the next number is 16.

__12__,

__12__,

__16__,

The last number must be 22, so that the range is 10.

__12__,

__12__,

__16__,

__22__