Box and Whisker Plots C. D. Toliver AP Statistics

Box and Whisker Box and Whisker PlotsPlots

C. D. ToliverC. D. Toliver

AP StatisticsAP Statistics

PercentilePercentile The percentile of a distribution of a set of data The percentile of a distribution of a set of data

is a value such that p% of the data fall at or is a value such that p% of the data fall at or below the data value and (100-p%) of the data below the data value and (100-p%) of the data fall at or above it. fall at or above it.

Example 1– suppose you scored 2000 on your Example 1– suppose you scored 2000 on your SAT and your score report said you fell in the SAT and your score report said you fell in the 8989thth percentile. Then 89% of the test takers percentile. Then 89% of the test takers scored a 2000 or less and 11% of the test scored a 2000 or less and 11% of the test takers scored 2000 or moretakers scored 2000 or more

Example 2 – The top 15% of the graduating Example 2 – The top 15% of the graduating class at WOS has a GPA of 3.9 or higher. That class at WOS has a GPA of 3.9 or higher. That means they are at least in the 85means they are at least in the 85thth percentile. percentile. 85 % of the students have a GPA of 3.9 or less.85 % of the students have a GPA of 3.9 or less.

QuartilesQuartiles

Special percentiles (100% divided Special percentiles (100% divided into fourths). So we consider data in into fourths). So we consider data in the the 2525thth percentile, quartile 1 (Q1) percentile, quartile 1 (Q1) Median or 50Median or 50thth percentile, quartile 2 percentile, quartile 2

(Q2)(Q2) 7575thth percentile, quartile 3 (Q3) percentile, quartile 3 (Q3)

How to Compute How to Compute QuartilesQuartiles

1.1. Order the data from smallest to largest.Order the data from smallest to largest.

2.2. Find the median. This is the second quartile, Find the median. This is the second quartile, Q2.Q2.

3.3. The first quartile Q1 is the median of the The first quartile Q1 is the median of the lower half of the data; that is, it is the lower half of the data; that is, it is the median of the data falling below Q2, but not median of the data falling below Q2, but not including Q2including Q2

4.4. The third quartile Q3 is the median of the The third quartile Q3 is the median of the upper half of the data; that is, it is the upper half of the data; that is, it is the median of the data falling above Q2 but not median of the data falling above Q2 but not including Q2including Q2

Example 1-Consider the Example 1-Consider the data set:data set:

{10, 20, 30 40, 50, 60, 70}{10, 20, 30 40, 50, 60, 70} The median, Q2 is 40The median, Q2 is 40 Q1 is the median of the values below Q1 is the median of the values below

40, These values are 10, 20, and 30. 40, These values are 10, 20, and 30. The median, or Q1 is 20.The median, or Q1 is 20.

Q3 is the median of the values above Q3 is the median of the values above 40, These values are 50, 60 and 70 40, These values are 50, 60 and 70 so the median or Q3 is 60.so the median or Q3 is 60.

Interquartile RangeInterquartile Range

The interquartile range is the The interquartile range is the difference between Q3 and Q1 or difference between Q3 and Q1 or Q3 –Q1Q3 –Q1

For our data set Q1 is 20, Q3 is 60, so For our data set Q1 is 20, Q3 is 60, so the interquartile range is 60-20 = 40the interquartile range is 60-20 = 40

Five-Number SummaryFive-Number Summary

Lowest Value or minimumLowest Value or minimum Q1Q1 MedianMedian Q3Q3 Highest value or maximumHighest value or maximum

Five-Number SummaryFive-Number Summary

Example - For the data set Example - For the data set {10,20,30,40,50,60,70}:{10,20,30,40,50,60,70}:

The five number summary isThe five number summary is Lowest number, 10Lowest number, 10 Q1, 20Q1, 20 Median, 40Median, 40 Q3, 60Q3, 60 Highest number, 70Highest number, 70

Box and Whisker PlotBox and Whisker Plot

A box and whisker plot is a graphical A box and whisker plot is a graphical display of the five number summarydisplay of the five number summary

Draw a scale to include the lowest and Draw a scale to include the lowest and highest data valueshighest data values

Draw a box from Q1 to Q3Draw a box from Q1 to Q3 Include a solid line through the box at Include a solid line through the box at

the medianthe median Draw solid lines, called whiskers from Draw solid lines, called whiskers from

Q1 to the lowest value and from Q3 to Q1 to the lowest value and from Q3 to the highest value.the highest value.

TI 84 1-Variable StatsTI 84 1-Variable Stats



TI 84 Box and Whisker TI 84 Box and Whisker PlotPlot






QuestionsQuestions

Is the median always in the middle of the Is the median always in the middle of the box of your box and whiskers plot?box of your box and whiskers plot?

How do outliers affect a box and whiskers How do outliers affect a box and whiskers plot?plot?

How can you use a box and whiskers plot How can you use a box and whiskers plot to tell if your data is skewed right or to tell if your data is skewed right or skewed left?skewed left?

What would be a better way to display the What would be a better way to display the data if you want to see the actual data if you want to see the actual outliers?outliers?

Example 2Example 2

Compute the five-number summary and Compute the five-number summary and draw a box and whiskers plot for the test draw a box and whiskers plot for the test scores on a recent AP Statistics testscores on a recent AP Statistics test

{76, 59, 76, 78, {76, 59, 76, 78, 100,66,63,70,89,87,81,48,78}100,66,63,70,89,87,81,48,78}

What scores if any might be considered What scores if any might be considered outliers?outliers?

How do they affect the shape of the graph?How do they affect the shape of the graph? How would the graph change if you How would the graph change if you

removed the outliers?removed the outliers?

Example 3Example 3 Compute the five-number summary and draw a Compute the five-number summary and draw a

box and whiskers plot for the test scores on a box and whiskers plot for the test scores on a recent AP Statistics test in another class.recent AP Statistics test in another class.

{87,78,91,70,70,66,87,78,80,86,97,98,97,94}{87,78,91,70,70,66,87,78,80,86,97,98,97,94} What scores if any might be considered What scores if any might be considered

outliers?outliers? How do they affect the shape of the graph?How do they affect the shape of the graph? How would the graph change if you removed How would the graph change if you removed

the outliers?the outliers? Compare the two sets of data? What can you Compare the two sets of data? What can you

conclude about the test results for the two conclude about the test results for the two classes?classes?

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Box and Whisker Plots C. D. Toliver AP Statistics