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Objective: Learn to find measures of variability. Course Variability

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Does the mean, median or mode give any indication of how the data is spread out or is it a central view of the data?

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5 Pieces of Data in Box & Whisker Plot (in order from left to right) 1.Lower extremelowest number 2.First quartilemiddle of lower-half 3.Medianmiddle number 4.Third quartilemiddle of upper half 5.Upper extremelargest number

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First quartile Third quartile Median Box and Whisker Plot Lower extreme Upper extreme

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Range--largest minus the smallest; its the entire length of the line

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Course Variability 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. Quartiles divide a data set into four equal parts. Heres how to find the 1 st and 3 rd quartiles: 1 st : order data least to greatest 2 nd : if odd amount, middle number is median If even amount, add 2 middle numbers and divide by 2 for median 3 rd : Divide data in half with a line; if odddont include median (draw line through it) if evendraw line between 2 middle data points 4 th : the first quartile is the middle half of the left side of data 5 th : the third quartile is the middle half of the right side of the data 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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Find the range and the first and third quartiles for the data set. Additional Example 1A: Finding Measures of Variability Course 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. Additional Example 1B: Finding Measures of Variability Course Variability B. 75, 61, 88, 79, 79, 99, 63, 77

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Find the range and the first and third quartiles for the data set. Try This: Example 1A Course Variability A. 25, 38, 66, 19, 91, 47, 13

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Course Variability B. 45, 31, 59, 49, 49, 69, 33, 47 Find the range and the first and third quartiles for the data set. Try This: Example 1B

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Course Variability 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: 21, 25, 15, 13, 17, 19, 19, 21 Additional Example 2: Making a Box-and-Whisker Plot Course Variability 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. Course Variability 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 Additional Example 2 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. Course Variability Step 3. Draw the box and whiskers. The left whisker is from the 1 st to 2 nd dot. The right whisker connects the 4 th and 5 th dot. The box connects the 2 nd dot and 4 th dot. Draw a line through the 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: Example 2 Course Variability Step 1. Order the data and find the smallest value, first quartile, median, third quartile, and largest value.

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

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Additional Example 3: Comparing Data Sets Using Box-and-Whisker Plots Course Variability These box-and-whisker plots compare the ages of the first ten U.S. presidents with the ages of the last ten presidents (through George W. Bush) when they took office. Note: 57 is the first quartile and the median.

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Additional Example 3 Continued Course Variability A. Compare the medians and ranges. The median for the first ten presidents is slightly greater. The range for the last ten presidents is greater. Note: 57 is the first quartile and the median.

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Additional Example 3 Continued Course Variability B. Compare the differences between the third quartile and first quartile for each. Note: 57 is the first quartile and the median.

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Try This: Example 3 Course Variability Final 1234T Oakland Tampa Bay These box-and- whisker plots compare the scores per quarter at Super Bowl XXXVII. The data in the T column is left out because it is a total of all the quarters. Oakland Tampa Bay

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Course Variability A. Compare the medians and ranges. Try This: Example 3 Continued Oakland Tampa Bay

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Course Variability B. Compare the differences between the third quartile and first quartile for each. Try This: Example 3 Continued Oakland Tampa Bay

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Lesson Quiz: Part 1 Find the range and the first and third quartile for each data set , 52, 68, 32, 53, 47, , 18, 11, 2, 7, 5, 9, 6, 13, 1, 17, 8, 0 Insert Lesson Title Here Course Variability

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Lesson Quiz: Part 2 Use the following data for problems 3 and 4. 91, 87, 98, 93, 89, 78, Make a box-and-whisker plot 4. What is the mean? Insert Lesson Title Here Course Variability

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