What could be the values in the data set?

Question

The median of a set of data is 2/3 of the greatest value and 1 2/5 of the least value. The data set has 7 numbers that are all whole numbers. The mean of the data set is equal to the median.

Answer 1

You can write the 7 numbers in order from least to greatest as  A, B, C, D, E, F, G  

 

The median is the middle value (D) which is 7/5 the least value  ==>  D = (7/5)A

The median is also 2/3 the greatest value  ==>  D = (2/3)G  

 

So (2/3)G = (7/5)A  ==>  G = (21/10)A  

 

If G and A are both whole numbers then A must be a multiple of 10  

 

So try A = 10 which implies that D = 14 and G = 21.  This gives the numbers as  

 

10, B, C, 14, E, F, 21  

 

If the mean is equal to the median then the sum of the numbers must be 7*14 = 98.  So pick whole numbers for B, C, E, and F that maintain the ordering and make the sum 98.  For example  

 

10, 11, 11, 14, 15, 16, 21  

 

If you don't want to repeat numbers then multiply everything by 2, subtract 1 from B and add 1 to F to get  

 

20, 21, 22, 28, 30, 33, 42  

Answer 2

A trick answer to this is that all seven number are zero.    Zero is a whole number, the mean and median are both zero and the conditions on the greatest and least in terms of the median are satisfied.   I looked for other solutions but did not find any.