Determine the median and quartiles of the following set of data: 56, 55, 90, 50, 41, 84, 68, 75, 92, 50, and 71.
First, it would be useful to go ahead and put these in ascending order, so from least to greatest. So we need to determine the median and the quartiles. The median is what separates the data into two equal parts. The quartiles are values that divide a set of data into four equal parts. So first, let’s find the median. If it’s gonna divide this data into two equal parts, they must be in the middle.
This would mean 68 is our median because there are five numbers to the left of it and five numbers to the right of it. It separated the data into two equal parts. So since we already have two equal parts and a quartile makes all equal parts, we need to cut these in half.
So 50 is a quartile and 84 will be a quartile because there are two numbers on each side of the quartiles. So there are four equal parts; each part has two numbers. 50 would be considered the lower quartile and 84 would be considered the upper quartile. Therefore, the median is 68, and the quartiles are 50 and 84.