# puzzle

#### osamastat

##### Member
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
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

Without writing anything on paper I don't think there is a unique a solution. I think we can define the possible values though.

#### katxt

##### Well-Known Member
How about x, 4-x, 7, 12, 12 with 0<x<2 as your data?

#### osamastat

##### Member
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
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.