Box-and-Whisker Plots

1. Box-and-Whisker Plots Making and Interpreting Box-and-Whisker Plots Becky Afghani LBUSD Math Office 2003

2. You will: Construct and Interpret Box and Whisker Plots

3. What is a Box-and Whisker Plot? Suppose you have a large set of data and want to know how it is distributed. Think of a teacher’s class set of test scores. A box-and-whisker plot displays the median, the quartiles, and the greatest and least values.

4. Why use a Box-and Whisker Plot? The box-and-whisker plot is a visual way to show the data. The median and quartiles can easily be read. The shape of the box and the whiskers gives information about how the numbers are spread out.

5. Who uses Box-and Whisker Plots? Scientists who perform experiments display their results using box-and-whisker plots. Medical researchers display their findings using box-and-whisker plots. Anyone who reads a scientific report needs to understand how a box-and-whisker works.

6. We will make a Box-and Whisker Plot Here are all of the test scores from your class on the last math test. (Not really!) 87 75 83 94 100 74 68 98 99 85 83 100 72 68 100

7. You will need a five-number summary in order to construct the box-and-whisker plot. Minimum ? Lower quartile (Q1) ? Median (Q2) ? Upper quartile (Q3) ? Maximum ?

8. Step 1: Write the data in order from least to greatest. 87 75 83 94 100 74 68 98 99 85 83 100 72 68 100 68, 68, 72, 74, 75, 83, 83, 85, 87, 94, 98, 99, 100, 100, 100

9. Step 2: Find the minimum and maximum values of the data. minimum maximum 68, 68, 72, 74, 75, 83, 83, 85, 87, 94, 98, 99, 100, 100, 100 The minimum is 68. The maximum is 100.

10. Tell your neighbor how to find the minimum and maximum. To find the minimum... To find the maximum...

11. Step 3: Find the median of the data. 7 in the lower half 7 in the upper half 1 in the middle 68, 68, 72, 74, 75, 83, 83, 85, 87, 94, 98, 99, 100, 100, 100 The median is 85.

12. Tell your neighbor how to find the median. To find the median...

13. Step 4: Find the lower quartile (Q1) of the data. lower half upper half The middle number is not in the lower or upper half. 68, 68, 72, 74, 75, 83, 83, 85, 87, 94, 98, 99, 100, 100, 100

14. Step 4: Find the lower quartile (Q1) of the data. lower half upper half 68, 68, 72, 74, 75, 83, 83, 85, 87, 94, 98, 99, 100, 100, 100 The lower quartile is 74.

15. Choral Response: What is the lower quartile? The median of the lower half The median of the lower half The median of the lower half The median of the lower half The median of the lower half

16. Step 5: Find the upper quartile (Q3) of the data. lower half upper half The middle number is not in the upper or Lower half. 68, 68, 72, 74, 75, 83, 83, 85, 87, 94, 98, 99, 100, 100, 100

17. Step 5: Find the upper quartile (Q3) of the data. lower half upper half 68, 68, 72, 74, 75, 83, 83, 85, 87, 94, 98, 99, 100, 100, 100 The upper quartile is 99.

18. Choral Response: What is the upper quartile? The median of the upper half The median of the upper half The median of the upper half The median of the upper half The median of the upper half

19. Now that we have our five-number summary, we can construct the box-and-whisker plot. Minimum 68 Lower quartile (Q1) 74 Median (Q2) 85 Upper quartile (Q3) 99 Maximum 100

20. Write in Your Notes:What are the five items in the five number summary? I can think of one... I bet he knows!

21. Step 6: Draw a number line that can show the data. 50 60 70 80 90 100 68, 68, 72, 74, 75, 83, 83, 85, 87, 94, 98, 99, 100, 100, 100

22. Step 7: Mark the minimum, maximum, median and both quartiles on the number line. Minimum 68 Lower quartile (Q1) 74 50 60 70 80 90 100 Median (Q2) 85 Upper quartile (Q3) 99 Maximum 100

23. Step 8: Draw a box between the lower and upper quartiles. Minimum 68 Lower quartile (Q1) 74 50 60 70 80 90 100 Median (Q2) 85 Upper quartile (Q3) 99 Maximum 100

24. Step 9: Draw a vertical line through the median. Minimum 68 Lower quartile (Q1) 74 50 60 70 80 90 100 Median (Q2) 85 Upper quartile (Q3) 99 Maximum 100

25. Step 10: Draw two “whiskers” from the quartiles to the minimum and maximum. Minimum 68 Lower quartile (Q1) 74 50 60 70 80 90 100 Median (Q2) 85 Upper quartile (Q3) 99 Maximum 100

26. Interpreting the box-and-whisker plot 25% 25% 25% 25% 50 60 70 80 90 100 Remember these are test scores. 25% of the test scores are in each whisker and each section of the box.

27. Find the false statement. 50 60 70 80 90 100 74 99 85 100 68 A) One fourth of the test scores were between 85 and 99. B) One half of the test scores were between 74 and 99. C) One half of the test scores were between 85 and 100. D) Three fourths of the test scores were between 68 and 85.

28. Make another box-and-whisker plot from this data: Age at First Inauguration of American Presidents from 1900 to 1999 4 2 3 6 1 1 1 2 4 4 5 5 6 6 5 6 0 1 2 4 9 42 is 42 years

29. Minimum and Maximum Age at First Inauguration of American Presidents from 1900 to 1999 4 2 3 6 1 1 1 2 4 4 5 5 6 6 5 6 0 1 2 4 9 42 is 42 years 42 is the minimum 69 is the maximum

30. Median What is halfway between 54 and 55? Age at First Inauguration of American Presidents from 1900 to 1999 ? 4 2 3 6 1 1 1 2 4 4 5 5 6 6 5 6 0 1 2 4 9 9th item 10th item 42 is 42 years How many data items are there? What is half of 18? 54.5 is the median 18 items

31. Lower Quartile Age at First Inauguration of American Presidents from 1900 to 1999 4 2 3 6 54.5 1 1 1 2 4 4 5 5 6 6 5 6 0 1 2 4 9 42 is 42 years How many items are in the lower half? 9 items Which item is in the middle? The 5th item 51 is the lower quartile

32. Upper Quartile Age at First Inauguration of American Presidents from 1900 to 1999 4 2 3 6 54.5 1 1 1 2 4 4 5 5 6 6 5 6 0 1 2 4 9 42 is 42 years How many items are in the upper half? The 5th item 9 items Which item is in the middle? 60 is the upper quartile

33. The Box-and-Whisker Plot Age at First Inauguration of American Presidents from 1900 to 1999 4 2 3 6 54.5 5 1 1 1 2 4 4 5 5 6 6 40 50 6 0 1 2 4 9 60 70 42 is 42 years

34. Find the false statement. 40 50 60 70 A) The oldest president at his inauguration was 69. B) One fourth of the presidents were 60 or over when inaugurated. C) One half of the presidents were inaugurated between ages 50 and 60. D) The youngest president to be inaugurated in the 1900s was 42.

35. Average Monthly High Temperatures in Anchorage, Alaska 0 0 10 10 20 20 30 30 40 40 50 50 60 60 70 70 80 80 90 90 100 100 Average Monthly High Temperatures in Long Beach, California Multiple Box-and-Whisker Plots Can Be Used to Compare Data Describe the variability between the data sets and compare the two 5 number summaries

36. Find the false statement. Average Monthly High Temperatures in Long Beach, California 100 0 0 10 10 20 20 30 30 40 40 50 50 60 60 70 70 80 80 90 90 100 Average Monthly High Temperatures in Anchorage, Alaska A) The range of average monthly high temperatures is broader in Anchorage than in Long Beach. B) The average monthly high temperatures in Long Beach are warmer than Anchorage. C) Half of the average monthly highs in Long Beach are between 27 and 59 degrees.

37. In your notes... 1. List the five items required for a box-and-whisker plot. 2. Write a short description for each.