Statistical Measures

Box-and-Whisker Plot5-Number SummaryInterquartile Range

We have looked at …

MeanMedianMode

They identify the centerThey represent the typical value

They are a one-number summary

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

Box-and-Whisker Plot

1. 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

2. It can help us visualize both the center and the spread of a data set

The 5-Number Summary

1. Min: The smallest value in the data set2. Q1: The cutoff point for the lowest 25% of

the data set (median of the lower half)3. Median: Separates the lower and upper

halves of the data set4. Q3: The cutoff point for the upper 25% of the

data set (median of the upper half)5. Max: The largest value in the data set

Finding the 5-Number Summary

42 37 3534 28 2613 25 25

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

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

30 28 33 29 37 3935 37 37 38 34 32

Wrapping It Up

Consider the following cities:

Atlanta Chicago Honolulu MinneapolisPhoenix Pittsburgh San Antonio San Diego

Which cities have more variation in temperature? Can you put them in order?

Atlanta Chicago Honolulu Minneapolis Phoenix Pittsburgh San Antonio San DiegoJanuary 41 21 73 12 54 26 49 57February 45 25 73 18 58 29 54 59March 54 37 74 31 62 39 62 60April 62 49 76 46 70 50 69 62May 69 59 78 59 79 60 76 64June 76 69 79 68 88 68 82 67July 79 73 81 74 94 72 85 71August 78 72 81 71 92 71 85 73September 73 64 81 61 86 64 79 71October 62 53 80 49 75 52 70 68November 63 40 77 33 62 42 60 62December 45 27 74 18 54 32 52 57

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:

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?