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# Box And Whisker Plots

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### Box And Whisker Plots

1. 1. 4-4<br />Variability<br />Course 3<br />Warm Up<br />1. Order the test scores from least to greatest: 89, 93, 79, 87, 91, 88, 92.<br />2. Find the median of the test scores.<br />Find the difference.<br />3. 17 – 0.9 4. 8.4 – 7. 6<br />16.1<br />3.4<br />5. 9.1 – 5.7 6. 190.3 – 23.4<br />
2. 2. 4-4<br />Variability<br />Course 3<br />Objective: Learnto find measures of variability.<br />
3. 3. 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?<br />
4. 4. 5 Pieces of Data in Box & Whisker Plot (in order from left to right)<br />Lower extreme—lowest number<br />First quartile—middle of lower-half<br />Median—middle number<br />Third quartile—middle of upper half<br />Upper extreme—largest number<br />
5. 5. 1 2 3 4 5 6 7 8 9<br />Box and Whisker Plot<br />Upper extreme<br />Lower extreme<br />Median<br />First quartile<br />Third quartile<br />
6. 6. 1 2 3 4 5 6 7 8 9<br />Range--largest minus the smallest; it’s the entire length of the line<br />
7. 7. 4-4<br />Variability<br />Third quartile: 5 median of upper half<br />First quartile: 3 median of lower half<br />Median: 4 (second quartile)<br />Course 3<br />Data<br />The range of a data set is the largest value minus the smallest value. For the kitten data, the range is 6 — 2 = 4.<br />Lower half<br />Upper half<br />2 3 3 3 3 3 3 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5 5 5 6<br />Quartilesdivide a data set into four equal parts. Here’s how to find the 1st and 3rd quartiles:<br />1st: order data least to greatest<br />2nd: if odd amount, middle number is median<br />If even amount, add 2 middle numbers and divide by 2 for median<br />3rd: Divide data in half with a line; if odd—don’t include median (draw line through it) if even—draw line between 2 middle data points<br />4th: the first quartile is the middle half of the left side of data<br />5th: the third quartile is the middle half of the right side of the data<br />
8. 8. 4-4<br />Variability<br />Course 3<br />Additional Example 1A: Finding Measures of Variability<br />Find the range and the first and third quartiles for the data set.<br />A. 15, 83, 75, 12, 19, 74, 21<br />Order the values.<br />12 15 19 21 74 75 83 <br />range: 83 – 12 = 71<br />first quartile: 15<br />third quartile: 75<br />
9. 9. 4-4<br />Variability<br />Course 3<br />Additional Example 1B: Finding Measures of Variability<br />Find the range and the first and third quartiles for the data set.<br />B. 75, 61, 88, 79, 79, 99, 63, 77<br />
10. 10. 4-4<br />Variability<br />Course 3<br />Try This: Example 1A<br />Find the range and the first and third quartiles for the data set.<br />A. 25, 38, 66, 19, 91, 47, 13<br />
11. 11. 4-4<br />Variability<br />Course 3<br />Try This: Example 1B<br />Find the range and the first and third quartiles for the data set.<br />B. 45, 31, 59, 49, 49, 69, 33, 47<br />
12. 12. 4-4<br />Variability<br /> 1 2 3 4 5 6 7 8 9<br />Course 3<br />A box-and-whiskerplot 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.<br />Median<br />First quartile<br />Third quartile<br />
13. 13. 4-4<br />Variability<br />15 + 17<br />2<br />21 + 21<br />2<br />third quartile: = 21<br />first quartile: = 16 <br />19 + 19<br />2<br />median: = 19<br />Course 3<br />Additional Example 2: Making a Box-and-Whisker Plot<br />Use the given data to make a box-and-whisker plot: <br />21, 25, 15, 13, 17, 19, 19, 21<br />Step 1. Order the data and find the smallest value, first quartile, median, third quartile, and largest value. <br />13 15 17 19 19 21 21 25<br />smallest value: 13<br />largest value: 25<br />
14. 14. 4-4<br />Variability<br />12 14 16 18 20 22 24 26 28<br />Course 3<br />Additional Example 2 Continued<br />Use the given data to make a box-and-whisker plot.<br />Step 2. Draw a number line and plot a point above each value from Step 1. <br />Step 1. Order the data and find the smallest value, first quartile, median, third quartile, and largest value. <br />13 15 17 19 19 21 21 25<br />smallest value 13<br />first quartile 16<br />third quartile 21<br />largest value 25<br />median<br /> 19<br />
15. 15. 4-4<br />Variability<br />12 14 16 18 20 22 24 26 28<br />Course 3<br />Use the given data to make a box-and-whisker plot.<br />Step 3. Draw the box and whiskers. The left whisker is from the 1st to 2nd dot. The right whisker connects the 4th and 5th dot. The box connects the 2nd dot and 4th dot. Draw a line through the median.<br />Step 2. Draw a number line and plot a point above each value. <br />13 15 17 19 19 21 21 25<br />
16. 16. 4-4<br />Variability<br />Course 3<br />Try This: Example 2<br />Use the given data to make a box-and-whisker plot. <br />31, 23, 33, 35, 26, 24, 31, 29<br />Step 1. Order the data and find the smallest value, first quartile, median, third quartile, and largest value. <br />
17. 17. 4-4<br />Variability<br />22 24 26 28 30 32 34 36 38<br />Course 3<br />Try This: Example 2 Continued<br />Use the given data to make a box-and-whisker plot.<br />Step 2. Draw a number line and plot a point above each value. <br />
18. 18. 4-4<br />Variability<br />22 24 26 28 30 32 34 36 38<br />Course 3<br />Try This: Example 2 Continued<br />Use the given data to make a box-and-whisker plot.<br />Step 3. Draw the box and whiskers. <br />Step 2. Draw a number line and plot a point above each value. <br />
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22. 22. 4-4<br />Variability<br />Course 3<br />Additional Example 3: Comparing Data Sets Using Box-and-Whisker Plots<br />Note: 57 is the first quartile and the median.<br />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. <br />
23. 23. 4-4<br />Variability<br />Course 3<br />Additional Example 3 Continued<br />Note: 57 is the first quartile and the median.<br />A. Compare the medians and ranges.<br />The median for the first ten presidents is slightly greater. The range for the last ten presidents is greater.<br />
24. 24. 4-4<br />Variability<br />Course 3<br />Additional Example 3 Continued<br />Note: 57 is the first quartile and the median.<br />B. Compare the differences between the third quartile and first quartile for each.<br />
25. 25. 4-4<br />Variability<br />Oakland<br />0 3 6 9 12 15 18<br />Tampa Bay<br />0 3 6 9 12 15 18<br />Course 3<br />Try This: Example 3<br />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.<br />
26. 26. 4-4<br />Variability<br />Oakland<br />0 3 6 9 12 15 18<br />Tampa Bay<br />0 3 6 9 12 15 18<br />Course 3<br />Try This: Example 3 Continued<br />A. Compare the medians and ranges.<br />
27. 27. 4-4<br />Variability<br />Oakland<br />0 3 6 9 12 15 18<br />Tampa Bay<br />0 3 6 9 12 15 18<br />Course 3<br />Try This: Example 3 Continued<br />B. Compare the differences between the third quartile and first quartile for each.<br />
28. 28. 4-4<br />Variability<br />Course 3<br />Insert Lesson Title Here<br />Lesson Quiz: Part 1<br />Find the range and the first and third quartile for each data set. <br />1. 48, 52, 68, 32, 53, 47, 51<br />2. 3, 18, 11, 2, 7, 5, 9, 6, 13, 1, 17, 8, 0<br />
29. 29. 4-4<br />Variability<br />Course 3<br />Insert Lesson Title Here<br />Lesson Quiz: Part 2<br />Use the following data for problems 3 and 4. 91, 87, 98, 93, 89, 78, 94<br />3. Make a box-and-whisker plot<br />4. What is the mean?<br />