Note that there are two boxplots available. The one that is highlighted is the one that will show
outliers. The calculator determines outliers by the 1.5(IQR) rule. Note that the data are in L2 for this
example. Once this screen is set up correctly, press ZOOM → 9:STAT to display the boxplot.example: Using the same dataset as the previous example, but replacing the 10.2 with 20, which
would be an outlier in this dataset (the largest possible non-outlier for these data would be 9.8
+ 1.5(9.8 – 3.9) = 18.65), we get the following graph on the calculator:Note that the “whisker” ends at the largest value in the dataset that is not an outlier, 13.Percentile Rank of a Term
The percentile rank of a term in a distribution equals the proportion of terms in the distribution less than
the term. A term that is at the 75th percentile is larger than 75% of the terms in a distribution. If we know
the five-number summary for a set of data, then Q1 is at the 25th percentile, the median is at the 50th
percentile, and Q3 is at the 75th percentile. Some texts define the percentile rank of a term to be the
proportion of terms less than or equal to the term. By this definition, being at the 100th percentile is
possible.
z-Scores
One way to identify the position of a term in a distribution is to note how many standard deviations the
term is above or below the mean. The statistic that does this is the z-score:
The z -score is positive when x is above the mean and negative when it is below the mean.