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Box and Whisker Plots

Box and Whisker Plots

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Box and Whisker Plots

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  1. Box and Whisker Plots Unit 2, Day 8 Adapted from the presentation at: http://www.quia.com/files/quia/users/donettec/BoxandWhiskerPlots.pptx

  2. Sample Data: 3, 5, 4, 2, 1, 6, 8, 11, 14, 13, 6, 9, 10, 7

  3. Put the numbers in order 1, 2, 3, 4, 5, 6, 6, 7, 8, 9, 10, 11, 13, 14

  4. Find the median 1, 2, 3, 4, 5, 6, 6, 7, 8, 9, 10, 11, 13, 14 6.5

  5. Find the lower quartile (Q1) 1, 2, 3, 4, 5, 6, 6, │7, 8, 9, 10, 11, 13, 14 1, 2, 3, 4, 5, 6, 6

  6. Find the upper quartile (Q3) 1, 2, 3, 4, 5, 6, 6, │7, 8, 9, 10, 11, 13, 14 1, 2, 3, 4, 5, 6, 6 7, 8, 9, 10, 11, 13, 14

  7. Draw a number line 1, 2, 3, 4, 5, 6, 6 | 7, 8, 9, 10, 11, 13, 14 1 2 3 4 5 6 7 8 9 10 11 12 13 14

  8. Draw the “box” and median 1, 2, 3, 4, 5, 6, 6 | 7, 8, 9, 10, 11, 13, 14 1 2 3 4 5 6 7 8 9 10 11 12 13 14

  9. Draw the “whiskers” 1, 2, 3, 4, 5, 6, 6 | 7, 8, 9, 10, 11, 13, 14 1 2 3 4 5 6 7 8 9 10 11 12 13 14

  10. Construct a box-and-whisker plot for the following test scores: 80, 75, 90, 95, 65, 65, 80, 85, 70, 100

  11. Find the 5 number summary: • Suppose you were to catch and measurethe length of 13 fish in a lake:

  12. But what does it mean? • Since the medians (three of them) represent the middle points, they split the data into four equal parts. In other words: • one quarter of the data numbers are less than 8.5 • one quarter of the data numbers are between 8.5 and 12 • one quarter of the data numbers are between 12 and 14 • one quarter of the data numbers are greater than 14

  13. Another Example: An advertising agency researched the ages of viewers most interested in various types of television ads. Consider the following summaries:

  14. The mean age of the people surveyed is approximately 50 years old. As a result, the producers of the show decided to obtain advertisers for a typical viewer of 50 years old. According to the table, what products or services do you think the producers will target? Based on the sample, what percent of the people surveyed would have been interested in these commercials if the advertising table were accurate?

  15. The show failed to generate interest the advertisers hoped. As a result, they stopped advertising on the show and the show was cancelled. Kristin made the argument that a better age to describe the typical viewer is the median age. What is the median age of the sample? What products or services does the advertising table suggest for viewers if the median age is considered as a description of the typical viewer?

  16. The difference between Q3 and Q1, or Q3 – Q1, is called the interquartile rangeor IQR. What is the interquartile range (IQR) for this data distribution? • The IQR is a number that specifies the length of the interval that contains the middle half of the ages of viewers. Do you think producers of the show would prefer a show that has a small or large interquartile range? Explain your answer. • Do you agree with Kristin’s argument that the median age provides a better description of a typical viewer? Explain your answer.

  17. One Last Example: Students at Waldo High School are involved in a special project that involves communicating with people in Kenya. Consider a box plot of the ages of 200 randomly selected people from Kenya:

  18. A box plot can be used to display extreme data values that are identified as outliers. • The “*” in the box plot are the ages of four people from this sample. Based on the sample, these four ages were considered outliers. • Estimate the values of the 4 ages represented by an “*”. • An outlier is defined to be any data value that is more than 1.5×(IQR) away from the nearest quartile.

  19. Homework: • Page NY736, #1-4, 8, 10, 11-15, 17 • http://www.regentsprep.org/regents/math/ALGEBRA/AD3/PracData.htm