Question

In the data set, n is an outlier and is the greatest number in the data set.

10 19 21 24 25 29 30 34 37 n

What is the least possible whole number value for n? @ganeshie8

Answer 1

let \(n\) be some large number and find the `median` and `IQR`

Answer 2

@ganeshie8 How do I find the median in an even amount of numbers, I can't remember?

Answer 3

take the average of middle two values

Answer 4

10 19 21 24 `25 29` 30 34 37 n

median (25+29)/2 = ?

Answer 5

Oh, uh... 27

Answer 6

Right! next find the IQR

Answer 7

IQR = Q3 - Q1

Answer 8

do you know how to find Q1, Q3 ?

Answer 9

21 and 30?

Answer 10

Q1 = 21 is correct

Q3 is wrong

Answer 11

`10 19 21 24 25` `29 30 34 37 n`


clearly 21 is the center of first half, so Q1 = 21
similarly 34 is the center of second half, so Q3 = 34

Answer 12

next find the IQR

Answer 13

sim[ply subtract Q1 from Q3 for IQR :
\[IQR = Q3-Q1 = 34-21 = 13\]

Answer 14

we call a data value is outlier if it is greater than `median + 1.5* IQR `

median = 27
IQR = 13

`median + 1.5*IQR` = 27 + 1.5*13 = 46.5

so the minimum possible whole nuumber value for n is 47 for it to be an outlier

Answer 15

So the answer is 47?

Answer 16

@ganeshie8

Answer 17

Yep!

Answer 18

Thanks!!

Answer 19

@ganeshie8 47 turned out to be wrong, it was 54. Thanks though! :)