Question

The data represents the mpg for vehicles manufactured by a company in the past 5 years. Find the third quartile, Q3, of the data. Data: 28.7, 25.5, 21.8, 21.6, 20.5, 16.7, 16.3, 15.4, 13.9.
A. 21.8
B. 25.5
C. 24.75
D. 23.65

Answer 1

OK. First put all the numbers in order.

Answer 2

So like starting from least to greatest right?

Answer 3

right

Answer 4

Okay. I got that done: 13.9, 15.4, 16.3, 16.7, 20.5, 21.6, 21.8, 25.5, 28.7.

Answer 5

ok, great. Does your book tell you how to compute quartiles, by the way? There isn't universal agreement on it. I can tell you how wikipedia says to do it, but it may not be the same as what your book says.

Answer 6

I don't have a book.

Answer 7

oh, where did the problem come from?

Answer 8

A worksheet. I forgot the book.

Answer 9

oh. Well, anyway, quartiles are what you get when you divide your list of data into 4 parts

Answer 10

So the 3rd quartile starts 3/4 of the way through the list.

Answer 11

So what you do to find the 3rd quartile is multiply the length of the list by 3/4, round up, and take that element of the list.

Answer 12

Ah I'm still confused :/ Can you give me an example, please?

Answer 13

Well let's take a simple list, 1 2 3 4 5 6 7 8 9. Going 1/4 of the way through the list, is 1/4 * 9 = 2.25, round up to 3. So the third element of the list (3) is the first quartile.

Answer 14

If the list is 100 200 300 400 500 600 700 800 900, you do the same thing. To find the 3rd quartile, you multiply the length of the list (9) times 3/4, and round up. You get 7. So the 3rd quartile is the 7th element of the list, which is 700.

Answer 15

So is it basically taking the last number and multiply that by 3/4 and then rounding the answer for that? Or did I understand that completely wrong?

Answer 16

well, not the last number, but the length of the list.

Answer 17

My first example was confusing - look at the second example (100 200 300...). In that case there are 9 elements in the list, so to find the 3rd quartile you multiply 3/4 * 9 and round up.

Answer 18

So counting how many numbers there are and take that and multiply it by 3/4? Or is that still wrong? I'm sorry, I get so confused when it comes to Algebra and Geometry and related things.

Answer 19

yep, you got it this time

Answer 20

so now try that on your original list.

Answer 21

Alright so I took 3/4*9 and I got 6 3/4.
I don't think that is right.. it doesn't seem like it.

Answer 22

nope, that's exactly right ... now round that up to 7, and take the 7th element of the sorted list.

Answer 23

So 21.8?

Answer 24

Yep, you got it!

Answer 25

Thank you! :)