106 CHAPTER 2 Descriptive Statistics Percentiles and Other Fractiles In addition to using quartiles to specify a measure of position, you can also use percentiles and deciles. Here is a summary of these common fractiles. Fractiles Summary Symbols Quartiles Divide a data set into 4 equal parts. Q1, Q2, Q3 Deciles Divide a data set into 10 equal parts. D1, D2, D3, c, D9 Percentiles Divide a data set into 100 equal parts. P1, P2, P3, c, P99 Percentiles are often used in education and health-related fields to indicate how one individual compares with others in a group. Percentiles can also be used to identify unusually high or unusually low values. For instance, children’s growth measurements are often expressed in percentiles. Measurements in the 95th percentile and above are unusually high, while those in the 5th percentile and below are unusually low. Interpreting Percentiles The ogive at the right represents the cumulative frequency distribution for SAT scores of college-bound students in a recent year. What score represents the 90th percentile? (Source: College Board) SOLUTION From the ogive, you can see that the 90th percentile corresponds to a score of 1350. Interpretation This means that approximately 90% of the students had an SAT score of 1350 or less. TRY IT YOURSELF 5 The points scored by the 55 winning teams in the Super Bowl (see page 39) are represented in the ogive at the left. What score represents the 65th percentile? How should you interpret this? Answer: Page A37 In Example 5, you used an ogive to approximate a data entry that corresponds to a percentile. You can also use an ogive to approximate a percentile that corresponds to a data entry. Another way to find a percentile is to use a formula. To find the percentile that corresponds to a specific data entry x, use the formula Percentile of x = number of data entries less than x total number of data entries # 100 and then round to the nearest whole number. DEFINITION EXAMPLE 5 Score Percentile SAT Scores 400 600 800 1000 1200 1400 1600 10 20 30 40 50 60 70 80 90 100 Study Tip Notice that the 25th percentile is the same as Q1; the 50th percentile is the same as Q2, or the median; and the 75th percentile is the same as Q3. Study Tip Be sure you understand what a percentile means. For instance, the weight of a six-month-old infant is at the 78th percentile. This means the infant weighs the same as or more than 78% of all six-month-old infants. It does not mean that the infant weighs 78% of some ideal weight. Points Percentile 12.5 Points Scored by Super Bowl Winner 19.5 26.5 33.5 40.5 47.5 54.5 61.5 10 20 30 40 50 60 70 80 90 100
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