16. Step 1 – Order Numbers Order the set of numbers from least to greatest.

17. Find the median. The median is the middle number. If the data has two middle numbers, find the mean of the two numbers. What is the median? Step 2 – Find the Median

18. Find the lower, or first quartile and upper, or third quartiles. These are considered the lower and upper medians. These are the middle numbers on each side of the median. What are they in this example? Step 3 – First & Third Quartiles

19. Interquartile Range The interquartile range is the difference between the upper quartile and the lower quartile. 14 – 8.5 =5.5

20. Now you are ready to construct the actual box & whisker graph. First you will need to draw an ordinary number line that extends far enough in both directions to include all the numbers in your data: Step 4 – Draw a Number Line

21. Locate the median using a vertical line just above your number line: Step 5 – Draw the Parts

22. Locate the first quartile and the third quartile with similar vertical lines: Step 5 – Draw the Parts

23. Next, draw a box using the lower and upper median lines as endpoints: Step 5 – Draw the Parts

24. Finally, the whiskers extend out to the data's smallest number, 5 and largest number, 20: Step 5 – Draw the Parts Outliers are not included in the box and whisker plot. They are shown as an asterisks on the number line. For example, if the data set had an outlier of 24, it would be show as seen below.

25. Step 6 - Label the Parts of a Box-and- Whisker Plot 123 54 Outliers are not included in the box and whisker plot. They are shown as an asterisks on the number line. MedianThird Quartile First Quartile Lower extreme Upper extreme2

26. Lower Quartile = 5½ Q1Q1 Upper Quartile = 9 Q3Q3 Median = 8 Q2Q2 456789101112 4, 4, 5, 6, 8, 8, 8, 9, 9, 9, 10, 12 Example 1: Draw a Box plot for the data below Drawing a Box Plot.

27. Upper Quartile = 10 Q3Q3 Lower Quartile = 4 Q1Q1 Median = 8 Q2Q2 3, 4, 4, 6, 8, 8, 8, 9, 10, 10, 15, Example 2: Draw a Box plot for the data below Drawing a Box Plot. 34567891011 1213 1415

28. Upper Quartile = 180 QuQu Lower Quartile = 158 QLQL Median = 171 Q2Q2 Question: Stuart recorded the heights in cm of boys in his class as shown below. Draw a box plot for this data. Drawing a Box Plot. 115, 148, 155, 158, 165, 166, 166, 171, 171, 173, 175, 180, 184, 186, 186 13 0 14 0 15 0 16 0 17 0 18 0 19 0 cm

29. Practice Use the following set of data to create a box plot. 3, 7, 11, 11, 15, 21, 23, 39, 41, 45, 50, 61, 87, 99, 220

30. Median What is the median or 2 nd quartile? 3, 7, 11, 11, 15, 21, 23, 39, 41, 45, 50, 61, 87, 99, 220 The median is 39

31. 1 st Quartile What is the 1 st quartile? 3, 7, 11, 11, 15, 21, 23, 39, 41, 45, 50, 61, 87, 99, 220 The lower quartile is 11

32. 3rd Quartile What is the 3 rd quartile? 3, 7, 11, 11, 15, 21, 23, 39, 41, 45, 50, 61, 87, 99, 220 The third quartile is 61

33. What is the Interquartile Range? 50

34. Outliers An outlier is a number that falls outside the limits. Are there any outliers? The outlier is 220

35. Upper Extreme What is the upper extreme? 3, 7, 11, 11, 15, 21, 23, 39, 41, 45, 50, 61, 87, 99, 220 The upper extreme is 99 c

36. Lower Extreme What is the lower extreme limit? 3, 7, 11, 11, 15, 21, 23, 39, 41, 45, 50, 61, 87, 99, 220 The lower extreme is 3

37. Graphing The Data Now use the data you have collected to create a box and whisker plot.

38. Independent Practice – Create box plots for the following data 12, 6, 4, 9, 8, 4, 9, 8, 5, 9, 8, 10 Example 1: Draw a box plot for the data below. 6, 3, 9, 8, 4, 10, 8, 4, 15, 8, 10 Example 2: Draw a box plot for the data below. Worksheet 1