1. Warm Up Problem 1 (Multiple Choice) Four friends take an IQ test. Their scores are 96, 100, 106, 114. Which of the following statements is true? I. The mean is 103. II. The mean is 104. III. The median is 100. IV. The median is 106. (A) I only (B) II only (C) III only (D) IV only (E) None is true 1

2. Test Your Understanding of This Lesson Solution The correct answer is (B). The mean score is computed from the equation: Mean score = Σx / n = (96 + 100 + 106 + 114) / 4 = 104 Since there are an even number of scores (4 scores), the median is the average of the two middle scores. Thus, the median is (100 + 106) / 2 = 103. 2

3. + STAT GAME PLAN Date 2/19/13 TU Trigonometry California Standard 8.0 Students organize and describe distributions of data by using …box-and- whisker plots. Goal Students will apply quartiles and five- number summary. Section / Topic 1.4a Quartiles Homework P34-35 (1-6, no 6g) Announcements Tutoring in Room 308 with Mrs Guntalilib Late Start Wednesday Quiz 1.4-1.6 on Tuesday 2/26

4. Quartiles The quartiles are the three numbers that divide the ordered data into four equally sized groups. Q 1 has 25% of the data below it. Q 2 has 50% of the data below it. (Median) Q 3 has 75% of the data below it. 4

5. Obtaining the Quartiles Order the data. Find the median (also called Q 2 ) Look at the lower half of values. The “median” of this lower half = Q 1 Look at the upper half of the data. The “median” of this upper half = Q 3 5

6. Illustrative example: 10 ages AGE (years) values, ordered array (n = 10): 05 11 21 24 27 28 30 42 50 52    Q1 Q2 Q3 Q1 = 21 Q2 = average of 27 and 28 = 27.5 Q3 = 42 6

7. Five-Number Summary Minimum Quartile 1 Median Quartile 3 maximum 7 Used to make box plots

8. I Do: Draw a Box and Whisker Plot for the flowing information. The following set of numbers are the amount of marbles fifteen different boys own. 18 27 34 52 54 59 61 68 78 82 85 87 91 93 100 Include all the following. a.In order from least to greatest if not already. b.Median c.1st (Lower) Quartile d.3rd (Upper) quartile e.Minimum f.Maximum g.Interquartile range h.Make a box-and-whisker plot for the data. 8

9. b. Median 18 27 34 52 54 59 61 78 82 85 87 91 93 100 I DO: 9 68

10. c. 1st (Lower) Quartile Next, we consider only the values to the left of the median: 18 27 34 52 54 59 61. We now find the median of this set of numbers. Remember, the median is the value exactly in the middle of an ordered set of numbers. I DO: 10

11. d. 3rd (Upper) quartile Now consider only the values to the left of the median: 78 82 85 87 91 93 100. We now find the median of this set of numbers. I DO: 11

12. g. interquartile range You are now ready to find the interquartile range (IQR). The interquartile range is the difference between the upper quartile and the lower quartile. Q 3 – Q 1 = 87-52= 35 I DO: 12

13. Drawing a Box-and-Whisker Plot 1.Find the five-number summary of the data set. 2.Construct a horizontal scale that spans the range of the data. 3.Plot the five numbers above the horizontal scale. 4.Draw a box above the horizontal scale from Q 1 to Q 3 and draw a vertical line in the box at Q 2. 5.Draw whiskers from the box to the minimum and maximum entries. 1.Find the five-number summary of the data set. 2.Construct a horizontal scale that spans the range of the data. 3.Plot the five numbers above the horizontal scale. 4.Draw a box above the horizontal scale from Q 1 to Q 3 and draw a vertical line in the box at Q 2. 5.Draw whiskers from the box to the minimum and maximum entries. Larson/Farber 4th ed.13 Whisker Maximum entryMinimum entry Box Median, Q 2 Q3Q3 Q1Q1

14. h. Draw the box and whisker plot. Median = 68 1 st (Lower) Quartile =52 3rd (Upper) quartile =87 Smallest value = 18 Largest value = 100 I DO: 14

15. h. Draw the box and whisker plot. I DO: 15

16. The test scores of 15 employees enrolled in a CPR training course are listed. Find the five number summary of the test scores and use it to create a box plot. 13 9 18 15 14 21 7 10 11 20 5 18 37 16 17 Larson/Farber 4th ed.16 You Do Together:

17. 5 7 9 10 11 13 14 15 16 17 18 18 20 21 37 Larson/Farber 4th ed.17 Q2Q2 Lower half Upper half Q1Q1 Q3Q3 About one fourth of the employees scored 10 or less, about one half scored 15 or less about three fourths scored 18 or less. You Do Together:

18. Draw a box-and-whisker plot that represents the 15 test scores. Recall Min = 5 Q 1 = 10 Q 2 = 15 Q 3 = 18 Max = 37 Larson/Farber 4th ed.18 510151837 Solution : About half the scores are between 10 and 18. By looking at the length of the right whisker, you can conclude 37 is a possible outlier. You Do Together:

19. 3.1 - 19 Heights from a Simple Random Sample of Women 1.What is the IQR (interquartile range)? 1.What percent of the data is between 61.5 inches to 64.95 inches? 2.What is the range? 3.Generally, 75% of women are shorter than how many inches? 4.If Jenn is approximately 67 inches tall, what quartile does she lie in? 1.What is the IQR (interquartile range)? 1.What percent of the data is between 61.5 inches to 64.95 inches? 2.What is the range? 3.Generally, 75% of women are shorter than how many inches? 4.If Jenn is approximately 67 inches tall, what quartile does she lie in? YOU DO ALONE: Q 3 – Q 1 = 64.95 – 61.5 = 3.45 Max – Min = 67.8 – 59.1 = 8.7 50%50% 64.95 inches Upper Quartile

20. 3.1 - 20 YOU DO: 1 2 3

21. 3.1 - 21 Multiple choice:

22. 3.1 - 22 Multiple Choice :

23. 3.1 - 23 Test scores on mastery of current technology. 1.What is the IQR (interquartile range)? 1.What percent of students scored greater than a 68? 2.What is the range? 3.What is the median of the test scores? 4.If Jess scored at 59 on the test, what quartile does she lie in? 5.Discussion: What are some explanations for the wide range of scores? 1.What is the IQR (interquartile range)? 1.What percent of students scored greater than a 68? 2.What is the range? 3.What is the median of the test scores? 4.If Jess scored at 59 on the test, what quartile does she lie in? 5.Discussion: What are some explanations for the wide range of scores? Lesson Quiz Q 3 – Q 1 = 87 – 52 = 35 Max – Min = 100 – 18 = 82 50%50% 6868 2nd Quartile