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Percentiles and Box-and-Whisker Plots

Learn how to interpret percentile scores, compute quartiles, make box-and-whisker plots, and describe data spread. Practice exercises included.

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Percentiles and Box-and-Whisker Plots

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  1. Section 3.3Percentiles and Box-and-Whisker Plots

  2. StatsWednesday, November 7 • Check – in homework • “Empirical Rule & Chebyshev’s Theorem” Worksheets • Notes – Section 3.3 • Percentiles • 5-Number Summaries • Box – and Whisker Plots • Work on Assignment Thursday: Quiz – Section 3.2 Friday: Review for Chapter 3 Test Monday: Chapter 3 Test

  3. Objectives After this section, you will be able to: • Interpret the meaning of percentile scores; • Compute the median, quartiles, and five-number summary from raw data; • Make a box-and-whisker plot. Interpret the results; • Describe how a box-and-whisker plot indicates spread of data about the median.

  4. Percentile • For whole numbers P ( where 1 ≤ P ≤ 99), the Pthpercentile of a distribution is a value such the __________ of the data fall _______________________ it and (100 – P)% of the data fall at or ___________________. See Figure 3-3 on pg 103 “A Histogram with the 60th Percentile”

  5. Guided Exercise You took the English achievement test to obtain college credit in freshman English by exam. • If your score is at the 89th percentile, what percentage of scores are at or below yours? • If the scores ranged from 1 to 100 and your raw score is 95, does this necessarily mean that your score is at the 95th percentile?

  6. Calculating Percentiles • There are _________ percentiles. In an ideal situation, the ________ percentiles divide the data into __________ equal parts. Lowest 1st 2nd 3rd 4th 5th 98th 99th Highest If the number of data points are not exactly divisible by _______, the percentiles ____________________________________________.

  7. Special Percentiles….Quartiles • Quartiles divide the data into ___________________. Quartile 1: Quartile 2: Quartile 3:

  8. How to Compute Quartiles • Order the data from smallest to largest; • Find the median. This is _________. • Find Q1 = the median of the _____________________ of the data (not including Q2). • Find Q3 = the median of the ______________________ of the data (not including Q2).

  9. Interquartile range IQR = _____________________________ …tells us the _____________ of the middle half of the data.

  10. Example Consumer Reports did a study of ice cream bars. 27 bars with taste ratings of the least “fair” were listed, and cost per bar was included in the report. Just how much will an ice cream bar cost? Bar sizes varied. Find the quartiles. Find the Interquartile range.

  11. A. Find the Quartiles 1. First, order the data from smallest to largest. Find the median. Since there are 27 data values, the median is the 14th value. median = Q2 = 0.50 Find Q1. There are 13 values below the median position. Q1 is the median of these values. It is the 7th value. First quartile = Q1 = 0.33 Find Q3. There are also 13 values about the median. Q3 is the median of these these values. It is the 7th value from the right end. Third quartile = Q3 = 1.00

  12. B. Find the interquartile range IQR = Q3 – Q1 = 1.00 – 0.33 = 0.67 This means that the middle half of the data has a cost spread of $0.67.

  13. PRACTICE A Consumer Reports article included the calorie count of the rated ice cream bars. There were 22 vanilla-flavored bars rated. Bars varied in size and some of the smaller bars had fewer calories. Find the quartiles. Find the Interquartile range.

  14. A. Find the quartiles.

  15. B. Find the interquartile range

  16. Five-Number Summary We use the 5-number summary to create a _________________________

  17. Box-and-Whisker Plot

  18. How to make a box-and-whisker plot • Draw a scale to include the lowest and highest data values. • Above the scale, draw a box from ___________________. • Include a _______________________ through the box at the _________________. • Draw horizontal lines, called ______________________, from Q1 to the lowest value and from Q3 to the highest value.

  19. Example Using the data from the last practice problem (calories in ice cream bars), make a box-and-whisker plot. Use the plot to make observations about the distribution of calories. Five-number summary from practice problem: Low value = 111; Q1 = 182; median = 221.5; Q3 = 319; high value = 439

  20. Practice: #5 on pg 109 • Homework: A#3.3 Page 110 #s 6 – 8 Due: ___Thursday, Nov 7_____

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