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
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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.
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