Question

describe how to estimate the IQR of a data set from a histogram.

Answer 1

Just as the median is the point that divides a distribution in half, quartiles are the points that divide a distribution into quarters. We will use the symbols Q1, Q2 and Q3 to represent the quartiles.
Note that Q2 = M, the median.

- The interquartile range
The interquartile range (IQR) is defined to be the spread of the middle 50% of data values,

so that:
IQR = Q3 − Q1

Answer 2

To calculate the IQR, it is necessary to first calculate the quartiles Q1 and Q3. In principle,
this is straight forward as:

Q1 is the midpoint of the lower half of the data values
Q3 is the midpoint of the upper half of the data values

Again, if the data has been ordered, the computation of the quartiles is relatively
straightforward.

Answer 3

can quartile 3 be the same number as quartile 2?

Answer 4

Nope.

Answer 5

Well, it depends, but usually its different.

Answer 6

ok, thanks for replying! in my teacher's math notes, it seems that the median is the same as the Q3, so i was confused

Answer 7

No worries. Also I encourage you to read this thoroughly, and you will hopefully understand it:

http://www.mathsisfun.com/data/quartiles.html

Answer 8

yes, i understand that part, but i can't apply it to histograms. in this math problem, the intervals of each bar of the histogram is from 50-54, 55-59, 60-64, and 65-69, so we have to estimate the iqr.

Answer 9

Yes, you're right! In histograms it is different for sure.

Answer 10

wait, if the link works, https://rmms.schoolloop.com/file/1407475294160/1213987969199/4376126647920378664.pdf, (its the first example that im confused on)

Answer 11

or let me take a screenshot and attach that file here.

Answer 12

The link does not work, but the screenshot will work. :)

Answer 13

Let me see ...

Answer 14

Thanks A LOT for helping me. I really appreciate it. I was stuck on this for a long time. So I don't understand how Q3 was found to find the IQR.

Answer 15

Hey, that's alright. I am here to help! =]

Answer 16

Give a moment, going over it ...

Answer 17

The way you do it is you use the midpoint of each range to represent that bar.
So there are three people ages 52, three people aged 57, five people aged 62, and two people ages 67 ...