Big Ideas Math Integrated I, 2016
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Big Ideas Math Integrated I, 2016 View details
2. Box-and-Whisker Plots
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Exercise 2 Page 339

See solution.

Practice makes perfect

To find how can we use a box-and-whisker plot to describe a data set, let's describe each of its elements. A box-and-whisker plot shows the variability of a data set along a number line. It uses a rectangular box and two segments. These segments are called whiskers.

  • The box extends from the first to the third quartiles (Q_1 and Q_3), with a line in the middle indicating the median (Q_2) of the data.
  • The first quartile is the median of the lower half of the data and the third quartile is the median of the upper half of the data.
  • The first segment extends from the least value of the data to Q_1, while the second one extends from Q_3 to the greatest value of the data.

    The set of numbers used to draw the box plot is called the five-number summary of the data set. Each of the five numbers is labeled accordingly.

    Boxplot shown above a number line

    Therefore, we can use a box-and-whisker plot to show the least value, first quartile, median, second quartile, and greatest value of a data set. Additionally, by only looking at the box-and-whisker plot, we can state some facts about the data set.

    • If the box and whisker to the left of the median are approximately of the same size than those to the right, the data is symmetric.
    • If the length of the box and whisker on the left of the median are a noticeably different size than those on the right, the data set is skewed.
    • If the whiskers are very long, the data might have outliers.
    • The difference between the greatest value and the least value indicates the range of the data set.
    • The difference between the third quartile and the first quartile indicates the interquartile range of the data set.