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Learn to find measures of variability. Box-and-whisker Plots

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The table below summarizes a veterinarian’s records for kitten litters born in a given year. Litter Size23456 Number of Litters While central tendency describes the middle of a data set, variability describes how spread out the data is. The range of a data set is the largest value minus the smallest value. Quartiles divide a data set into four equal parts.

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Litter Size23456 Number of Litters The range of a data set is the largest value minus the smallest value. For the kitten data, the range is 6 — 2 = 4. The range is affected by outliers, so another measure is often used. Quartiles divide a data set into four equal parts. Kitten Data Lower halfUpper half First quartile: 3 median of lower half Third quartile: 5 median of upper half Median: 4 (second quartile)

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A box-and-whisker plot shows the distribution of data. The middle half of the data is represented by a “box” with a vertical line at the median. The lower fourth and upper fourth quarters are represented by “whiskers” that extend to the smallest and largest values. First quartile Third quartile Median

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Use the given data to make a box- and-whisker plot. 31, 23, 33, 35, 26, 24, 31, 29 Try This: Step 1. Order the data and find the smallest value, first quartile, median, third quartile, and largest value. smallest value: 23 largest value: 35 first quartile: = third quartile: = median: =

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Use the given data to make a box-and- whisker plot Step 2. Draw a number line and plot a point above each value

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Step 2. Draw a number line and plot a point above each value. Use the given data to make a box-and-whisker plot Step 3. Draw the box and whiskers

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Find the range and the first and third quartiles for the data set. Finding Measures of Variability A. 15, 83, 75, 12, 19, 74, Order the values. range: 83 – 12 = 71 first quartile: 15 third quartile: 75

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Find the range and the first and third quartiles for the data set. Finding Measures of Variability B. 75, 61, 88, 79, 79, 99, 63, range: 99 – 61 = 38 first quartile: = third quartile: = Order the values.

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Use the given data to make a box-and-whisker plot: 21, 25, 15, 13, 17, 19, 19, 21 Making a Box-and-Whisker Plot Step 1. Order the data and find the smallest value, first quartile, median, third quartile, and largest value smallest value: 13 largest value: 25 first quartile: = third quartile: = median: =

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Step 1. Order the data and find the smallest value, first quartile, median, third quartile, and largest value. Use the given data to make a box-and-whisker plot Step 2. Draw a number line and plot a point above each value from step 1. smallest value first quartile 16 median 19 third quartile 21 largest value 25 Continued:

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Step 2. Draw a number line and plot a point above each value. Use the given data to make a box-and-whisker plot Step 3. Draw the box and whiskers Continued:

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Lesson Quiz Use the following data for problems 3 and 4. 91, 87, 98, 93, 89, 78, Make a box-and-whisker plot 2. What are the 3 quartiles? 87, 91,

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