Statistical measures   box plots
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  • 1. Statistical Measures
    Box-and-Whisker Plot
    5-Number Summary
    Interquartile Range
  • 2. We have looked at …
    Mean
    Median
    Mode
    They identify the center
    They represent the typical value
    They are a one-number summary
  • 3. It’s not enough to know the middle
    “A statistician is the only one who can have his head in the freezer and his feet in burning coals and say that on average he feels fine.”
    Anonymous
  • 4. Box-and-Whisker Plot
    A box-and-whisker plot gives a graphic presentation of data using five measures:
    The median
    The first and third quartiles
    The smallest and largest values
    It can help us visualize both the center and the spread of a data set
  • 5.
  • 6. The 5-Number Summary
    Min: The smallest value in the data set
    Q1: The cutoff point for the lowest 25% of the data set (median of the lower half)
    Median: Separates the lower and upper halves of the data set
    Q3: The cutoff point for the upper 25% of the data set (median of the upper half)
    Max: The largest value in the data set
  • 7. Finding the 5-Number Summary
    Find the five number summary for the following average number of vacation days in selected countries. (Source: World Tourism Organization)
    With an odd-number of data elements
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  • 24. Finding the 5-Number Summary
    Shown here is the number of new theater productions that appeared on Broadway for the past several years (Source: League of American Theaters and Producers, Inc.)
    With an even-number of data elements
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  • 32. Wrapping It Up
    Consider the following cities:
    Which cities have more variation in temperature? Can you put them in order?
  • 33. Select one of the cities above. Find the 5-Number Summary for average monthly temperatures and construct a box plot for that city below:
    Min: Q1: Median: Q3: Max:
  • 34. Combine your results with other students and answer the following questions:
    Which city had the lowest average temperature?
     
    Which city had the highest average temperature?
     
    Which city had the lowest median temperature?
     
    Which city had the highest median temperature?
     
    Which city had the largest range of temperatures?
     
    Which city had the smallest range of temperatures?