2.3. Box-and-Whisker Plots http://www.ck12.org
TABLE2.27:(continued)
Lake/Reservoir % of Capacity
Lake Mohave 85
Lake Mead 95
Lake Powell 89Figure:Arizona Reservoir Capacity, 12 / 31 / 98.Source:http://www.seattlecentral.edu/qelp/sets/008/008.html
This data was collected in 1998 and the water levels in many states have taken a dramatic turn for the worse. For
example, Lake Powell is currently at less than 50% of capacity^1.
Placing the data in order from smallest to largest gives:
3 , 9 , 33 , 49 , 51 , 59 , 85 , 89 , 95 , 98
With 10 numbers, the median would be between 51 and 59, or 55. Recall that the lower quartile is the 25thpercentile,
or where 25% of the data is below that value. In this data set, that number is 33. Similarly, the upper quartile is 89.
Therefore the five-number summary is:
{ 3 , 33 , 55 , 89 , 98 }
Box-and-Whisker Plots
Abox-and-whisker plotis a very convenient and informative way to represent single-variable data. To create the
“box” part of the plot, draw a rectangle that extends from the lower quartile to the upper quartile. Draw a line through
the interior of the rectangle at the median. Then we connect the ends of the box to the minimum and maximum values
using a line segment to form the “whisker”. Here is the box plot for this data:
The plot divides the data into quarters. If the number of data points is divisible by 4, then there will be exactly the
same number of values in each of the two whiskers, as well as the two sections in the box. In this example, because
there are 10 data points, it will only be approximately the same, but approximately 25% of the data appears in each
section. You can also usually learn something about theshapeof the distribution from the sections of the plot. If
each of the four sections of the plot is about the same length, then the data will be symmetric. Of course, it could be
uniform or bimodal also, so you would have to also look at a dot plot or histogram to get a more complete picture of
the shape.