Find five numbers so that the mean, median, mode and range are all 4?

1 Answer
Mar 7, 2018

Answer:

The example set could be:

#S={2,4,4,4,6}#

See explanation.

Explanation:

First you can notice that if the set was:

#S_1={4,4,4,4,4}#

then it would fulfill 2 conditions: mean and median, but

  1. the set does not have the mode because all numbers are the same,

  2. the range is zero (again all numbers are the same)

To have the mode the set would have to have at least one element different from #4#, but if we changed only one element the mean would change, so at least two numbers need to be changed to keep mean equal to #4#..

Now to get the range the difference between the changed numbers should be #4#. That leads us to adding two to one number and subtracting two from the other.

Finally we can get the set from the answer.