Question

Which is the interquartile range of the data set: 6, 8, 10, 12, 14?

Answer 1

The IQR is Q3-Q1. So first you need find those. Did you do so yet?

Answer 2

No. I don't know how to do it

Answer 3

Ok - do you know what the median of this data set is?

Answer 4

well i know the mean is 12.5 and the median is 10 right?

Answer 5

Yes, median is 10.

Now, do you know how to find Q3 (the third quartile)? and Q1?

Answer 6

noo thats what im having trouble with

Answer 7

The easiest way to think of it is this:

Let the median (which also happens to be Q2) "split" the data in 2. Then Q3 is the median of the upper half, and Q1 is the median of the lower half.

Answer 8

hrmm.. im lost. what do you mean by split the data in 2?

Answer 9

oh okay thank you. thats much better haha

Answer 10

The median is the "halfway point" of all the data observations. So now, look at the lower half, and look at the upper half. Find the median of each half (as if it is it's own data set). Those are your Q1, and Q3.

Answer 11

lol you're welcome. :)

Answer 12

Once you have Q3 and Q1, then IQR is just: Q3 - Q1

Answer 13

sorry im slow.. how do you find the nedian of each half?

Answer 14

would i just add it and divide it by how many numbers there are the way i find my median before it was split?

Answer 15

if thats what im supposed to do, i got 6+8/2=7 and 12+4/2=13. then i just did Q3-Q1 like you said. and that got me 6

Answer 16

Yes, since there are an even number of observations, you add the middle two (I know there are ONLY two, but the general rule is to add the "middle two" so just stressing that rule here), and divide by 2.

If there are an odd number of observations, you take the "middle" observation (that should be how you got 10 as the median).

For an even number, you have to average the middle two.