My Work:

Okay so the IQR is the range of the middle half of the data set, or the difference between the third and first quartiles.

I lined up the numbers from least to greatest:

10, 12, 14, 15, 15.5, 16, 17.5, 18, 19

Then I found the first and third quartiles.

Min Q1 Q2 Q3 Max

10, 12, 14, 15, 15.5, 16, 17.5, 18, 19

So then I did 17.5 - 14 = 3.5 This doesn't match any of the choices above.

awsometrunt14 Feb 7, 2019

#1**+1 **

10 12 14 15 15.5 16 17.5 18 19

Q2 = 15.5

Q1 = [12 + 14] / 2 = 26 / 2 = 13

Q3 = [ 17.5 + 18 ] / 2 = 17.75

So....the IQR is just 17.75 - 13 = 4.75

CPhill Feb 7, 2019

#2**+1 **

Can you tell me why those numbers had to be added so I know for future questions like this?

awsometrunt14
Feb 7, 2019

#3**+2 **

We are actually finding 3 medians

The first is the median of the data set = 15.5 = Q2

Then....we look at the four data points to the left of Q2

These are 10 12 14 15

The median of these = [ 12 + 14]/2 = 13 = Q1

And then we do the same thing with the four data points to the right of Q2

These are 16 17.5 18 19

The median of these = [ 17.5 + 18 ] / 2 = 17.75 = Q3

So....the IQR = Q3 - Q1 = 4.5

Hope that helps

CPhill
Feb 7, 2019