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Boxplots. Why use boxplots?. ease of construction convenient handling of outliers construction is not subjective (like histograms) Used with medium or large size data sets (n > 10) useful for comparative displays. Disadvantage of boxplots. does not retain the individual observations
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Why use boxplots? ease of construction convenient handling of outliers construction is not subjective (like histograms) Used with medium or large size data sets (n > 10) useful for comparative displays
Disadvantage of boxplots does not retain the individual observations should not be used with small data sets (n < 10)
How to construct find five-number summary Min Q1 Med Q3 Max draw box from Q1 to Q3 draw median as center line in the box extend whiskers to min & max
Modified boxplots display outliers fences mark off mild & extreme outliers whiskers extend to largest (smallest) data value insidethefence ALWAYS use modified boxplots in this class!!!
Inner fence Interquartile Range (IQR) – is the range (length) of the box Q3 - Q1 Q1 – 1.5IQR Q3 + 1.5IQR Any observation outside this fence is an outlier! Put a dot for the outliers.
Modified Boxplot . . . Draw the “whisker” from the quartiles to the observation that is within the fence!
Outer fence Any observation between the fences is considered a mild outlier. Q1 – 3IQR Q3 + 3IQR Any observation outside this fence is an extreme outlier!
For the AP Exam . . . . . . you just need to find outliers, you DO NOT need to identify them as mild or extreme. Therefore, you just need to use the 1.5IQRs
A report from the U.S. Department of Justice gave the following percent increase in federal prison populations in 20 northeastern & mid-western states in 1999. 5.9 1.3 5.0 5.9 4.5 5.6 4.1 6.3 4.8 6.9 4.5 3.5 7.2 6.4 5.5 5.3 8.0 4.4 7.2 3.2 Create a modified boxplot. Describe the distribution. Use the calculator to create a modified boxplot.
Symmetrical boxplots Approximately symmetrical boxplot Skewed boxplot
Evidence suggests that a high indoor radon concentration might be linked to the development of childhood cancers. The data that follows is the radon concentration in two different samples of houses. The first sample consisted of houses in which a child was diagnosed with cancer. Houses in the second sample had no recorded cases of childhood cancer.
Cancer 10 21 5 23 15 11 9 13 27 13 39 22 7 20 45 12 15 3 8 11 18 16 23 16 9 57 16 21 18 38 37 10 15 11 18 210 22 11 16 17 33 10 No Cancer 9 38 11 12 29 5 7 6 8 29 24 12 17 11 11 3 9 33 17 55 11 29 13 24 7 11 21 6 39 29 7 8 55 9 21 9 3 85 11 14 Create parallel boxplots. Compare the distributions.
Cancer’s 5 # Summary: No Cancer’s 5 # Summary: Min Q1 Med Q3 Max 3 11 16 22 210 IQR = 18 IQR = 11 Min Q1 Med Q3 Max 3 8.5 11.5 26.5 85
Calculating the fence (Cancer): Q1 – 1.5 IQR 11 – 1.5*11 = - 5.5 Q3 + 1.5 IQR 22 + 1.5*11 = 38.5 Calculating the fence (No Cancer): Q1 – 1.5 IQR 8.5 – 1.5*18 = -18.5 Q3 + 1.5 IQR 26.5 + 1.5*18 = 53.5
Creating a Box Plot Cancer No Cancer 0 50 100 150 200 Radon
Cancer No Cancer 200 100 Radon The median radon concentration for the no cancer group is lower than the median for the cancer group. The range of the cancer group is larger than the range for the no cancer group. Both distributions are skewed right. The cancer group has outliers at 39, 45, 57, and 210. The no cancer group has outliers at 55 and 85.
