Question

Find five numbers so that the mean, median, mode and range is 4.​

Answer 1

Answer:

Let’s break this apart

Well we know the median has to be 4

Since it’s 5 numbers the middle number has to be 4 since its the median.

Let’s put in what we know.

a, b, 4, d, e

Constraints:

There has to be more then 1 “4”.

e-a = 4

So using that information lets solve since the possibility is almost endless

SO lets make e 5 and a 1.

1, b, 4, d, 5

There has to be more then 1 4 so lets put that as b.

We can solve for the last remaining digits.

1+ 4 + 4 + d + 5 / 5 = 4

14 + d /5 = 4

2.2 + d = 4

1.8 = d

So now if we put in order and replace b with 1.8 and make d as the previous “b” as 4.

1, 1.8, 4, 4, 5

Thats your 5 numbers right there.

Check:

Mode is 4: yes!

Range is 4: 5-1 = 4 yes!

Median is 4: yes!

Mean is 4: 1 + 1.8 + 4 + 4 +5 / 5 = 4 yes!

Every thing checks out.

There could be a lot of possibilities.

For example take this wrong one

Lets make the same exact thing except change the a and the e.

THis is what we have,

a, b, 4, d, e

Lets make e and a as 6 and 2.  6-2 is still 4 so its possible.

2, b, 4, d, 6

And of course we need more then 1 4 so lets make d 4.

2, b, 4, 4, 6

Now solve for b in the mean.

2 + b + 4 + 4 + 6  / 5 = 4

16 +b /5 = 4

3.2 + b = 4

Solve

B = 0.8

This doesn’t work cause the median and the range has constraint here…

When doing a median, it has to be in ORDER.

2, 0.8, 4, 4 , 6 isn’t in order

ANd even when put in order.

0.8, 2, 4, 4, 6

THe range has the constraint here becuase 6 - 0.8 isn’t 4.