puzzle

#1
if we 5 people , the mean of their wages is 7000 and the median has the same value. where the value of the mode is 12000, what is the value of range?

my question is there any relationship between those measures??!!
 

katxt

Well-Known Member
#2
Not for small samples. There are any number of 5 number sets which have those properties but with different ranges.
For large samples and well behaved data Mean – Mode = 3 (Mean – Median) is often approximately true.
 

Dason

Ambassador to the humans
#3
Without writing anything on paper I don't think there is a unique a solution. I think we can define the possible values though.
 
#5
Not for small samples. There are any number of 5 number sets which have those properties but with different ranges.
For large samples and well behaved data Mean – Mode = 3 (Mean – Median) is often approximately true.
but, what about the range!!...is there any relationship between range and this equation : Mean – Mode = 3 (Mean – Median)
 

katxt

Well-Known Member
#6
No, not really.
In your case, if the wages have to be whole numbers of thousands, then there is only 1 solution 1 3 7 12 12 and you take the range of those numbers.
 

Dason

Ambassador to the humans
#7
I was thinking the same thing. If we have a positive integer restriction then there is a unique solution but otherwise no.