The inter-quartile range of a set of numbers is the difference between its upper and lower quartile range. To find it, we need to firstly order the numbers from lowest to greatest. Your set of numbers would look like this:
74 74 76 82 86 88 90 92 94 96
To find the location of the upper quartile range, use the expression:
3/4(n+1) —> where n is the number of numbers in your set
So the expression looks like:
3/4(10+1)
Which equals 8.25, meaning the upper quartile will be between the 8th and 9th number in the set. If you count it, that will be between 92 and 94. You then have to get the mean between these two numbers which is 93.
Now you have to find the lower quartile. For that, use the formula:
1/4 (n + 1) —> where n is the number of numbers in your set
When you plug in the numbers you get
1/4(10+1)
Which is 2.75, meaning the lower quartile will be between the 2nd and 3rd position. These are 74 and 76. The mean of these two numbers is 75.
So your upper quartile is 93 and your lower quartile is 75.
