There are positions in a dataset that give us valuable information about the dataset. The five-number
summary of a dataset is composed of the minimum value, the lower quartile, the median, the upper
quartile, and the maximum value.
On the TI-83/84, these are reported on the second screen of data when you do 1-Var Stats as: minX
, Q1 , Med , Q3 , and maxX .
example: The following data are standard of living indices for 20 cities: 2.8, 3.9, 4.6, 5.3, 10.2,
9.8, 7.7, 13, 2.1, 0.3, 9.8, 5.3, 9.8, 2.7, 3.9, 7.7, 7.6, 10.1, 8.4, 8.3. Find the 5-number summary
for the data.
solution: Put the 20 values into a list on your calculator and do 1-Var Stats . We find:
minX=0.3, Q1=3.9, Med=7.65, Q3=9.8 , and maxX=13 .Boxplots (Outliers Revisited)
In the first part of this chapter, we discussed three types of graphs: dotplot, stemplot, and histogram. Using
the five-number summary, we can add a fourth type of one-variable graph to this group: the boxplot . A
boxplot is simply a graphical version of the five-number summary. A box is drawn that contains the
middle 50% of the data (from Q1 to Q3) and “whiskers” extend from the lines at the ends of the box (the
lower and upper quartiles) to the minimum and maximum values of the data if there are no outliers. If
there are outliers, the “whiskers” extend to the last value before the outlier that is not an outlier. The
outliers themselves are marked with a special symbol, such as a point, a box, or a plus sign.
The boxplot is sometimes referred to as a box and whisker plot.
example: Consider again the data from the previous example: 2.8, 3.9, 4.6, 5.3, 10.2, 9.8, 7.7, 13,
2.1, 0.3, 9.8, 5.3, 9.8, 2.7, 3.9, 7.7, 7.6, 10.1, 8.4, 8.3. A boxplot of this data, done on the TI-
83/84, looks like this (the five-number summary was [0.3, 3.9, 7.65, 9.8, 13]):
Calculator Tip: To get the graph above on your calculator, go to the STAT PLOTS menu, open one of the
plots, say Plot1 , and you will see a screen something like this: