Determine the median and quartiles of the following set of data: 1.8, 1.6, 1.1, 2.4, 0.6, 1.3, 2.9, 1.5, 0.4, 1.9, and 2.9.
The median will be the middle number found in the set of data. And then the quartiles will be the middle of the bottom half and the middle of the upper half.
So to do this, we need to arrange our numbers from least to greatest. Our smallest is 0.4 then 0.6, 1.1, 1.3, 1.5, 1.6, 1.8, 1.9, 2.4, 2.9, and once again 2.9. So in order to find the median and the quartiles, we need to count how many numbers there are: one, two, three, four, five, six, seven, eight, nine, 10, 11.
Therefore, the median, the middle number, of these 11 will be the sixth one. So our median is equal to 1.6. So there are five numbers on our lower half and five numbers on the upper half. And the middle of five numbers would be the third number. So the third number would be 1.1. That would be the lower quartile. And the upper quartile will be the third number in that set, so seven, eight, nine. Nine will be the third number. So 2.4 is the upper quartile. So, overall, the median is 1.6 and the quartiles are 1.1 and 2.4.