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Box-and-Whisker Plots

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Important Terms Median:The middle number in a set of data when the data are arranged in numerical order. Quartile:One of four equal parts of data from a large set of data. Upper Quartile:The median of the upper half of a set of numbers. Lower Quartile:The median of the lower half of a set of numbers. Lower Extreme:The least number in a set of data. Upper Extreme:The greatest number in a set of data. Outliers:Data that is more than 1.5 times the inner quartile range, from the quartiles.

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Step 1 Put the data in order from the least to the greatest. Data: Automobile gas mileages 12 17 19 20 22 23 24 24 27 29 31 34 39 45 48 27 12 23 45 24 39 19 48 24 20 22 29 17 34 31 Find the median - 24

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Step 2 Find the median of the first half of the data 12 17 19 20 22 23 24 24 27 29 31 34 39 45 48 20 This is called the Lower Quartile LQ -

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Step 3 Find the median of the upper half of the data 12 17 19 20 22 23 24 24 27 29 31 34 39 45 48 34 This is called the Upper Quartile UQ - Inter Quartile Range - the difference between the UQ and the LQ 34 - 20 = 14IR = UQ - LQ

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Step 4a Find the lowest number 12 17 19 20 22 23 24 24 27 29 31 34 39 45 48 12 This is called the Lower Extreme LE - Find the highest number This is called the Upper Extreme 48UE - Step 4b

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Step 5 12 17 19 20 22 23 24 24 27 29 31 34 39 45 48 Draw and label a number line with your 5 points. 10162228344046 LEUEUQLQMedian

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Step 5 continued Draw a box starting at the lower quartile and ending at the upper quartile. 10162228344046 Draw a vertical line through the median value.

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Step 5 continued Draw a line from the lowest number to the lower quartile and one from the highest number to the upper quartile. 10162228344046 “The Whiskers”

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A box - and - whisker plot divides data into four equal parts that represent 25% of the data 10162228344046 25% of the data falls between the LE and the LQ. 25% of the data falls between the LQ and the median. 25% of the data falls between the median and the UQ. 25% of the data falls between the UQ and the UE.

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You Try It! Make a box-and-whisker plot for the following recent test scores. 98 75 69 96 85 74 98 79 83 90 62 74 84 86

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62 69 74 74 75 79 83 84 85 86 90 96 98 98 83.5 Note: Because there is an even number of data, you have to take the average of the two middle numbers to determine the median. Median - Lower Quartile - 74 Upper Quartile - 90 Lower Extreme - 62 Upper Extreme - 98

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5060708090100 Recent Test Scores

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