Hey there! I'm happy to help!
The IQR is how far apart the first and third quartiles are, which are the middle numbers of the first and second halves of a data set. Let's find some random numbers that are 17 apart. We will use 3 and 20.
Now, we have to create a data set where 3 is the middle number of the first half and 20 is the middle number of the second half. Let's have one with six numbers because that's a good amount I guess. Remember that the data has to be going from least to greatest.
In our first half we will have one number that is smaller than 3 and one bigger than three so that 3 is in the middle. Here's an example of what our first half should look like:
2,3,5
Now, for our second half, we need a number smaller than 20 and one greater than 20 so 20 is the the middle. Here's the second half I've made for you.
16,20,100
So, the data set I've created for you is 2,3,5,16,20,100. However, there are many other possibilities as you've seen.
My answers for your question 1 and 2 are in the explanation I've done, and here's the math that shows that the interquartile range is 17.
You split the data in half.
2,3,5, 16,20,100
Q1 is the middle number of the first, which is 3. Q3 is the middle of the second, which is 20.
You find how far apart they are by subtracting 3 from 20.
20-3=17.
The IQR is 17.
Have a wonderful day! :D
