# What there's numbers have a range of 3, median of 3 and a mean of 3?

Relevance

Range is the difference between the highest and lowest numbers.

Median is the middle number.

Mean is the average.

I think you want *three* numbers.

Let's call them a, b, c

The range is 3 so:

c - a = 3

The median is 3, so the middle number (b) is 3

b = 3

The mean (average) is 3 so:

(a + b + c)/3 = 3

Take this last equation and substitute in b=3:

(a + c + 3)/3 = 3

Multiply both sides by 3

a + c + 3 = 9

Subtract 3 from both sides:

a + c = 6

a + c = 6

-a + c = 3

-------------

.... 2c = 9

c = 4½

And finally figure out a:

c - a = 3

4½ - a = 3

a = 1½

{1½, 3, 4½}

• First of all, because the median is 3, we know that if we write the numbers in numerical order, the middle number has to be 3.

Because the mode is 3, there must be at least one other 3, and since we are writing this in numerical order, a 3 must at least occupy a place on one side of the middle 3.

1st number: Has to be equal to, or less than 3

2nd number: Has to be equal to, or less than 3

3rd number: Has to be 3

4th number: Has to be equal to, or greater than 3

5th number: Has to be greater than 3 (if the largest number was 3, the mean could not be 4)

Hope that helps,

d.tcom