Create a box-and-whisker plot by finding the middle, upper and lower medians of a given data set to determine the position of each quartile. Use the corresponding numbers to mark the beginning and the end of the two boxes and two whiskers.
Start by ordering the data set from least to greatest. For example, a set consisting of 10, 7, 3, 9, 5, 16, 10, 13, 4, 8, and 11, would be rearranged as follows: 3, 4, 5, 7, 8, 9, 10, 10, 11, 13 and 16.
Since the data set has 11 numbers, its median is the sixth number in the list. Hence the number 9 divides the plot in half, with one group of numbers below it and another above. It also pinpoints the end of the first box and the beginning of the second.
The median of the numbers below 9 corresponds to the beginning of the first box, and the median of the numbers above 9 corresponds to the end of the second box.
The numbers below 9 are 3, 4, 5, 7 and 8, so the first box begins at the middle number, which is 5. The numbers above 9 are 10, 10, 11, 13 and 16, so the second box ends at the number in the middle of this group, which is 11.
The first whisker begins at 3, the smallest number, and it ends at 5, where the first box begins. The second whisker begins at 11, where the second box ends, and terminates at 16, the largest number. This divides the entire data set into four sections, or quartiles.