1. SDAP1.1 Know various forms of display for data sets, including a stem-and-leaf plot or box-and-whisker plot; use the forms to display a single set of data or to compare two sets of data. SDAP1.3 Understand the meaning of, and be able to compute, the minimum, the lower quartile, the median, the upper quartile, and the maximum of a data set. California Standards

2. Objective: Today we will display and analyze data in box-and-whisker plots.

3. APK Teacher I do 1. Order the test scores from least to greatest: 89, 93, 79, 87, 91, 88, 92. 2. Find the median of the test scores. 79, 87, 88, 89, 91, 92, 93 89 Find the median of the following test scores? 65, 75, 92, 90, 74, 86, 98 Students complete: We will need to know how to find the median in order to make box and whisker plots.

4. Vocabulary lower quartile upper quartile box-and-whisker plot minimum maximum

5. 78 85 88 88 89 90 92 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 box extends to the upper and lower quartiles. The upper quartile is the median of the upper half of the data. The lower quartile is the median of the lower half of the data. Lower quartile Upper quartile Median Data set: 85,92,78,88,90,88,89 What is a box-and-whisker plot? What are the upper and lower quartiles?

6. 78 85 88 88 89 90 92 The lower fourth and upper fourth quarters are represented by “whiskers” that extend to the minimum (least) and maximum (greatest) values. Lower quartile Upper quartileMedian Data set: 85,92,78,88,90,88,89 W hat are minimum and maximum values?

7. Litter Size23456 Number of Litters 168111 The table below summarizes a cat breeder’s records for kitten litters born in a given year. You can divide the data into four equal part using quartiles.

8. Kitten Data 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 Lower halfUpper half Lower quartile: 3 median of lower half Upper quartile: 5 median of upper half Median: 4 You know that the median of a data set divides the data into a lower half and an upper half. The median of the lower half is the lower quartile, and the median of the upper half is the upper quartile.

9. Kitten Data 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 Lower halfUpper half Lower quartile: 3 median of lower half Upper quartile: 5 median of upper half Median: 4 You know that the median of a data set divides the data into a lower half and an upper half. The median of the lower half is the lower quartile, and the median of the upper half is the upper quartile.

10. 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 Lower halfUpper half A B c D E F How do you know? What letter is the _____?

11. Importance Why do we need to know how to display and analyze data in box-and-whisker plots ? *It helps you to interpret and represent data. *It gives a visual representation of data. Tell your partner which reason is most important to you. You can use one of mine or one of your own. p/s - volunteers

12. Find the lower and upper quartiles for the data set. A. 15, 83, 75, 12, 19, 74, 21 12 15 19 21 74 75 83 Order the values. lower quartile: 15 upper quartile: 75 1.Order the data from least to greatest. 2.Find the median. 3.Find the median of the lower half – lower quartile 4.Find the median of the upper half – upper quartile I do How did I find the lower and upper quartiles?

13. Find the lower and upper quartiles for the data set. B. 75, 61, 88, 79, 79, 99, 63, 77 61 63 75 77 79 79 88 99 lower quartile: = 69 63 + 75 2 upper quartile: = 83.5 79 + 88 2 Order the values. 1.Order the data from least to greatest. 2.Find the median. 3.Find the median of the lower half – lower quartile 4.Find the median of the upper half – upper quartile We do

14. Find the lower and upper quartiles for the data set. A. 25, 38, 66, 19, 91, 47, 13 13 19 25 38 47 66 91 Order the values. lower quartile: 19 upper quartile: 66 1.Order the data from least to greatest. 2.Find the median. 3.Find the median of the lower half – lower quartile 4.Find the median of the upper half – upper quartile We do

15. B. 45, 31, 59, 49, 49, 69, 33, 47 31 33 45 47 49 49 59 69 Order the values. Find the lower and upper quartiles for the data set. lower quartile: = 39 33 + 45 2 upper quartile: = 54 49 + 59 2 1.Order the data from least to greatest. 2.Find the median. 3.Find the median of the lower half – lower quartile 4.Find the median of the upper half – upper quartile You do

16. 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 Step 1. Order the data from least to greatest. Then find the minimum, lower quartile, median, upper quartile, and maximum. 13 15 17 19 19 21 21 25 minimum: 13 maximum: 25 lower quartile: = 16 15 + 17 2 upper quartile: = 21 21 + 21 2 median: = 19 19 + 19 2 I do:

17. Use the given data to make a box-and-whisker plot. 12 14 16 18 20 22 24 26 28 Step 2. Draw a number line and plot a point above each value from Step 1. 13 15 17 19 19 21 21 25 Additional Example 2 Continued I do (cont.)

18. Use the given data to make a box-and-whisker plot. 12 14 16 18 20 22 24 26 28 Step 3. Draw the box and whiskers. 13 15 17 19 19 21 21 25 Additional Example 2 Continued I do (cont.)

19. 23 24 26 29 31 31 33 35 Use the given data to make a box-and-whisker plot. 31, 23, 33, 35, 26, 24, 31, 29 Check It Out! Example 2 Step 1. Order the data from least to greatest. Then find the minimum, lower quartile, median, upper quartile, and maximum. minimum: 23 maximum: 35 lower quartile: = 25 24 + 26 2 upper quartile: = 32 31 + 33 2 median: = 30 29 + 31 2 We do

20. Use the given data to make a box-and-whisker plot. 22 24 26 28 30 32 34 36 38 Step 2. Draw a number line and plot a point above each value. 23 24 26 29 31 31 33 35 Check It Out! Example 2 Continued We do (cont.)

21. Step 2. Draw a number line and plot a point above each value. Use the given data to make a box-and-whisker plot. 22 24 26 28 30 32 34 36 38 Step 3. Draw the box and whiskers. 23 24 26 29 31 31 33 35 Check It Out! Example 2 Continued We do (cont.)

22. Step 1. Order the data from least to greatest. Then find the minimum, lower quartile, median, upper quartile, and maximum. Step 2. Draw a number line and plot a point above each value. Step 3. Draw the box and whiskers. Additional Guided Practice: With partners: Page 544 #1 You do: Page 544 #2

23. Closure Find the lower and upper quartiles for each data set. 1. 48, 52, 68, 32, 53, 47, 51 lower = 47; upper = 53 What uses upper and lower quartiles, the median, the maximum, and the minimum to show a set of data?

24. Closure (cont.) Use the following data for problems 3 and 4. 91, 87, 98, 93, 89, 78, 94 3. Make a box-and-whisker plot. 78 87 91 94 98 What did you learn today about box-and-whisker plots?