Quartiles and Boxplots

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Unit 4

• Quartiles and Boxplots

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Five Number Summary

• Another very convenient way to graph quantitative
  data is a boxplot which uses 5 numbers to
  summarize the data
• Minimum value
• 25th percentile (1st quartile) Q1
• 50th percentile (2nd quartile or median) Q2
• 75th percentile (3rd quartile) Q3
• Maximum value

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Poverty Data for the 50 states and D. C.

• Interactive for finding the median and quartiles
  graphically
• A-5 Uses 2

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Why Boxplots?

• Present information more compactly than
  histograms
• Easier to make comparisons among several data
  sets

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Main Components of a Boxplot

• The boxplot represents the data of a random
  sample of women who took an exam in elementary
  statistics

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• lower quartile is 76.61 left side of the box
• upper quartile is 89.59 right side of the box
• median is 84.70 middle line of the box
• fences bound all the data except for outliers

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The Interquartile Range

• The interquartile range is a measure of how
  spread out the middle 50 of the data is
• Interquartile range (IQR) Upper Quartile -
  Lower Quartile
• IQR 89.59 - 76.61 12.98
• So, there is a spread of about 13 points in the
  middle 50 of the exam scores

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Outliers

• Compute
• lower quartile - 1.5 (IQR)
• 76.76 - 1.5(12.98) 57.29
• any data value below 57.29 is a low outlier
• upper quartile 1.5(IQR)
• 89.59 1.5(12.98) 109.06
• any data value above 109.06 is a high outlier

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Fences

• Lower fence is the smallest data value that is
  not an outlier
• Upper fence is the largest data value that is not
  an outlier

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Interpret the BoxplotRefer to Poverty Data Set

• Q1 10.2 Median 12.4 Q3 15.6
• IQR ? Lower fence ? Upper fence ?
• Outliers ?

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Calorie Content of Major Brands of Hotdogs
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Warnings

• Stem-and-leaf plots can be unwieldy for large
  data sets.
• Stem-and-leaf plots do not allow us to adjust for
  differing sample sizes when comparing two or more
  samples.
• The exact values of data cannot be obtained from
  a histogram.
• Boxplots can hide the mode and any clusters in
  the data.