Question

Please help



Create a set of data with 5 numbers that satisfy all of the following conditions:

1. the range is 10

2. the mean is 20

3. the median is 22

Answer 1

Please help. I dont know how to do this. :(

Answer 2

@astrangecat
Do you understand the meaning of the terms range, mean and median?

Answer 3

@mathmate

Yes

Answer 4

Can you give me three numbers with a mean of 20?

Answer 5

The mean is the average, the median is the middle value of the set of numbers, and the range is the difference between the largest and smallest number in the data set.

10 20 30 @mathmate

Answer 6

So can you tell me the range, mean, and median of 10,20,30?

Answer 7

@mathmate

The range is 20 the mean is 20 and the median is 20

Answer 8

Beautiful!
Can you change the numbers so that they have a range of 10, and yet keeping both mean and median at 20?

Answer 9

@mathmate

15 20 and 25?

Answer 10

Good! :)
Next step, we need a median of 22.
Can you add two numbers so that the median is 22, range still 10, and don't worry about the mean for now?

Answer 11

This is the part I get really lost on ...

Answer 12

17 22 and 27?

Answer 13

Oh, what I meant was to \(add\) two more numbers to 15,20,25 to make the median 22.
Your range is ok with 15 and 25. This way we will have 5 numbers as required. But don't worry about the mean for now. Recall that median is the middle number of the sorted list.

Answer 14

Ohhh okay,

so then 15 20 22 24 25?

Answer 15

Sure, can you please check the mean median and range again (after each change of numbers)

Answer 16

@mathmate

Alright,

The mean is 106

the range is 10

and the median is 22

Answer 17

sorry the mean is 21.2

Answer 18

That's not a problem. We have range 10, median 22 so far.
Mean is easy to fix.
We want a mean of 20 for 5 numbers. What should be the total of the five numbers?

Answer 19

@mathmate

The total should be 100

Answer 20

Exactly, what's our total so far?

Answer 21

@mathmate

106

Answer 22

Yep, so we're over by 6.
Any ideas as to what to do to take it down to a hundred, while keeping the range and median?

Answer 23

So the numbers should be

15 18 20 22 25?

Answer 24

No nvm then the median isnt 22

Answer 25

Nope, you're changing the median to 20! think of other ways!

Answer 26

@mathmate
14 17 22 23 24

Answer 27

That would make the mean 20

The range 10 and the median 22.

Answer 28

Eureka! You did it! Wow! Congrats!

Answer 29

@mathmate

Thank you so much!

Answer 30

You're welcome! :)