Building Your First Box Plot

Start with a real data set: the number of books read over summer by 5 students: 2, 4, 6, 8, 10. Step one, always: put the values in order from least to greatest. They already are here, so the very middle value, 6, is the medianThe middle value of a data set when the values are ordered from least to greatest.. The median splits the data set into a lower half, {2, 4}, and an upper half, {8, 10}.

Now find the middle of each half. The middle of the lower half, {2, 4}, is 3, and that's the first quartileOne of the values that divides an ordered data set into four equal-sized groups.. The middle of the upper half, {8, 10}, is 9, and that's the third quartile. The smallest value in the whole set, 2, is the lower extremeThe least value in a data set, shown at the left end of a box plot., and the largest, 10, is the upper extremeThe greatest value in a data set, shown at the right end of a box plot.. Put all five numbers together, 2, 3, 6, 9, 10, and you have the five-number summary, the exact numbers you need to draw a box plotA diagram that displays a numerical data set using five key values: the lowest number, first quartile, median, third quartile, and highest number.: a box from the first quartile to the third quartile, a line inside it at the median, and whiskers stretching out to the lower and upper extremes.

Adapted from Studio Aletheia's The Center for Quantitative Studies curriculum library, drawing on mathematical resources and the SC CCR Mathematics Standards.