Suppose the 5 numbers are a,b,c,d,e
where a ≤ b ≤ c ≤ d ≤ e
Then:
1. c=5 since it is the median and the median is the middle number when
there are an odd number of numbers, and 5 is an odd number of numbers.
2. a=b=4 since the mode is 4. Reasoning: There must be more 4's than
anything else. 4 is less than 5, and there must be more than 1 4.
But there can only be two numbers less than 5, and that can only be
if a=b=4. (We also know that d and e must be different and greater
than 5, but we may not need that.)
3. e-a=7 since the range is 7, and since a=4, e-4=7, so e=11
So a=4, b=4, c=5, d=?, e=11
4. (a+b+c+d+e)/5=6 since the mean is 6. Therefore
(4+4+5+d+11)/5=6
(24+d)/5=6
24+d=30
d=6
So the numbers are 4,4,5,6,11
Edwin
