15.2 Percentiles, Quartiles, & Box-and-Whisker Plots

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Presentation transcript:

15.2 Percentiles, Quartiles, & Box-and-Whisker Plots

Percentiles are a useful way to locate an item of data in a distribution The kth percentile of a distribution is a value such that k% of the distribution falls at or below the value. The kth percentile is often denoted Pk where k is an integer between 1 and 99. Ex 1) In a class of 600 students, Mei Li ranks 120th and Stan ranks 275th. Find their respective percentiles. Since Mei Li ranks 120th, 480 students rank below her (600 – 120) Mei Li is at the 80th percentile, P80 Since Stan ranks 275th, 325 students rank below him (600 – 275) Stan is at the 54th percentile, P54 *Note: Percentiles are rounded to nearest percent Several scores may have the same percentile

Ex 2) James scored in the 74th percentile on a test Ex 2) James scored in the 74th percentile on a test. If 685 students took the test, about how many students scored above James? 74% scored below or even with James (.74)(685) = 506.9 685 – 507 = 178 About 178 students scored above James *Bonus: Can you determine 3 other numbers that are in the 74th percentile for the data? 504, 505, 506, 508, 509, or 510

An important percentile is P50, the median, which locates the middle of a set of ordered data. odd number of data points  middle term even number of data points  average of 2 middle terms A quartile divides each half in half Lower quartile, Q1, is median of data below overall median Upper quartile, Q3, is median of data above overall median Ex 3) For the data set: {56, 78, 90, 85, 67, 66, 82, 94, 81, 80, 77, 69, 64, 90, 80} Find a) the median b) Q1 c) Q3 Order the data: 56, 64, 66, 67, 69, 77, 78, 80, 80, 81, 82, 85, 90, 90, 94 Q1 median Q3

Box-and-Whisker Plot: graphical presentation of data * Q1 & Q3 are called hinges box whisker whisker Q1 M Q3 Lower extreme Upper extreme Interquartile range Box-and-Whisker Plots can be vertical or horizontal Ex 4) median: Q1: Q3: Lower extreme: Upper extreme: Interquartile range: 16 14 20 3 31 20–14 = 6

Ex 5) The high temperatures in degrees Fahrenheit on the days of November in a Midwestern city were: 36, 32, 40, 33, 28, 27, 30, 28, 25, 24, 30, 24, 24, 22, 22, 25, 19, 20, 26, 21, 24, 27, 24, 26, 28, 30, 26, 25, 22, 19 Order the data: 19, 19, 20, 21, 22, 22, 22, 24, 24, 24, 24, 24, 25, 25, 25, 26, 26, 26, 27, 27, 28, 28, 28, 30, 30, 30, 32, 33, 36, 40 Median = Q1 = 24 L.E. = 19 Q3 = 28 U.E. = 40 Vertical box-and-whisker

Homework #1502 Pg 808 #1, 4–6, 7–11 odd, 14–16, 21–26, 29–32, 34