Determine the upper and lower quartiles of the following set of data: 114, 103, 50, 52, 95, 103, 93, 53, 65, 57, 52, 89, 111, 89, and 96.
We first need to put these number in ascending order from smallest to largest. Our smallest number is 50, then 52, then another 52, 53, 57, 65, 89, 89, 93, 95, 96, 103, 103, 111. And then lastly our largest number is 114. Here we have 15 numbers. And the median will be the middle number. And the middle number of 15 would be eight. There are seven numbers on each side.
Now to find the upper and lower quartiles, we need to find the middle of the lower half and the middle of the upper half. So here we have our lower half and our upper half. The middle number of seven, the fourth number, would be the lower quartile. It’s the middle of the seven numbers. So 53 is our lower quartile. And then the 12th number will be the upper quartile. So 103 is the upper quartile. So once again, our final answer will be that the lower quartile is 53 and the upper quartile is 103.