This document discusses box and whisker plots and the 5-number summary used to describe data distributions. A box and whisker plot depicts the minimum, lower quartile, median, upper quartile, and maximum of a dataset using a box and whiskers. Outliers are defined as values more than 1.5 times the interquartile range below the first quartile or above the third quartile. The document provides an example comparing temperatures from 2005 and 2008 using a box and whisker plot.

1. 5-number summary Minimum, Lower quartile, Quartiles are relatively insensitive to unusual values Median (second quartile), Upper quartile, and Interquartile range = Q 3 – Q 1 Maximum.

2. For example 25 55 59 59 63 71 71 74 80 80 80 83 84 84 87 88 95 95 100 100 Minimum Lower Quartile (Q1) Median Upper Quartile (Q3) Maximum

3. Boxplot (box and whiskers diagram) Depicts the 5-number summary Useful for comparing to data sets.

4. Components Number line extends from the theoretical (or practical) minimum value to the theoretical (or practical) maximum A box spans the lower and upper quartiles Dotted line through the box at the median Whiskers extend from the box to the minimum and maximum

5. Outliers Outliers are: Less than the lower quartile minus the 1.5 times the inter-quartile range, or Greater than upper quartile plus 1.5 times the interquartile range

6. Live Example Minimum First Quartile (Q1) Median Third Quartile (Q3) Maximum

7. Your turn Use a box and whiskers diagram to compare the 2005 and 2008 September temperatures Daily high temperatures for Trenton Identify any outliers 79 79 83 82 83 85 91 86 85 75 73 77 76 68 66 70 73 78 83 84 81 90 82 89 90 86 78 75 75 86 90 88 92 90 77 81 81 73 74 74 68 83 91 81 68 75 75 68 70 81 73 72 74 66 65 71 69 70 71

8. Two Ways to Characterize Data x i < X – 2s x i > X + 2x x i < Q1 – 1.5  IQR x i > Q3 + 1.5  IQR Outliers Distribution spread, frequency diagram, bar chart and Box and whiskers diagram Picture X and s Minimum, first quartile, median, third quartile, maximum Statistics Mean and standard deviation 5-number summary