1 / 23

Warm Up

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.

peri
Download Presentation

Warm Up

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

  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.

  3. Quartiles • The quartiles are the three numbers that divide the ordered data into four equally sized groups. • Q1 has 25% of the data below it. • Q2 has 50% of the data below it. (Median) • Q3 has 75% of the data below it.

  4. Obtaining the Quartiles • Order the data. • Find the median (also called Q2 ) • Look at the lower half of values. The “median” of this lower half = Q1 • Look at the upper half of the data. The “median” of this upper half = Q3

  5. Illustrative example: 10 ages AGE (years) values, ordered array (n = 10): 05 11 21 24 27 28 30 42 50 52 Q1Q2Q3 Q1 = 21 Q2 = average of 27 and 28 = 27.5 Q3 = 42

  6. Five-Number Summary • Minimum • Quartile1 • Median • Quartile3 • maximum Used to make box plots

  7. 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. In order from least to greatest if not already. Median 1st (Lower) Quartile 3rd (Upper) quartile Minimum Maximum Interquartile range Make a box-and-whisker plot for the data.

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

  9. I DO: 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.

  10. I DO: 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.

  11. I DO: g. interquartile range You are now ready to find the interquartilerange (IQR). The interquartile range is the difference between the upper quartile and the lower quartile. Q3 – Q1 = 87-52= 35

  12. Drawing a Box-and-Whisker Plot Box Whisker Whisker Minimum entry Maximum entry Q1 Median, Q2 Q3 Larson/Farber 4th ed. Find the five-number summary of the data set. Construct a horizontal scale that spans the range of the data. Plot the five numbers above the horizontal scale. Draw a box above the horizontal scale from Q1 to Q3 and draw a vertical line in the box at Q2. Draw whiskers from the box to the minimum and maximum entries.

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

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

  15. You Do Together: Larson/Farber 4th ed. 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

  16. You Do Together: Lower half Upper half Q2 Q1 Q3 About one fourth of the employees scored 10 or less, about one half scored 15 or less about three fourths scored 18 or less. Larson/Farber 4th ed. 5 7 9 10 11 13 14 15 16 17 18 18 20 21 37

  17. You Do Together: Solution: 5 10 15 18 37 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. Larson/Farber 4th ed. Draw a box-and-whisker plot that represents the 15 test scores. Recall Min = 5 Q1 = 10Q2 = 15 Q3 = 18Max = 37

  18. YOU DO ALONE: Heights from a Simple Random Sample of Women What is the IQR (interquartile range)? What percent of the data is between 61.5 inches to 64.95 inches? What is the range? Generally, 75% of women are shorter than how many inches? If Jenn is approximately 67 inches tall, what quartile does she lie in? Q3 – Q1 = 64.95 – 61.5 = 3.45 50% Max – Min = 67.8 – 59.1 = 8.7 64.95 inches Upper Quartile

  19. YOU DO: 1 2 3

  20. Multiple choice:

  21. Multiple Choice:

  22. Lesson Quiz Test scores on mastery of current technology. What is the IQR (interquartile range)? What percent of students scored greater than a 68? What is the range? What is the median of the test scores? If Jess scored at 59 on the test, what quartile does she lie in? Discussion: What are some explanations for the wide range of scores? Q3 – Q1 =87–52= 35 50% Max – Min =100–18=82 68 2nd Quartile

More Related