Can you find other sets of five positive whole numbers where:
Mean = Median = Mode = Range
3,6,6,6,9
5 numbers: 6 numbers: 4 numbers:
A. Mode < Median < Mean 2,2,3,7,8 2,2,2,4,9,9 2,2,3,13
B. Mode < Mean < Median 1,1,3,4,5 1,1,1,5,5,6 1,1,6,7
C. Mean < Mode < Median impossible impossible impossible
D. Mean < Median < Mode 1,2,4,5,5 1,1,2,4,4,4 1,2,6,6
E. Median < Mode < Mean impossible 3,4,5,7,7,34 impossible
F. Median < Mean < Mode 1,2,7,35,35 3,4,5,6,7,7 1,2,4,4
Not all of these can be satisfied by sets of five numbers! Can you explain why?
C is impossible because if the Median is greater than the Mode then the Mode numbers must be the 2 smallest numbers. However the Mean is stated to be smaller than the 2 smallest numbers which is impossible since the average (Mean) will always be greater than (or equal to) the smallest number/s in any given set of numbers.
E is impossible because if the Mode is greater than the Median then the Mode numbers must be the 2 biggest numbers. However if the Mean is the biggest of them all it must be greater than the Mode numbers which we previously explained to be the biggest numbers. This is impossible because the Mean will always be less than (or equal to) the biggest number/s in any given set of numbers.