Elementary Statistics: A Step-by-Step Approach with Formula Card 9th Edition

Published by McGraw-Hill Education
ISBN 10: 0078136334
ISBN 13: 978-0-07813-633-7

Chapter 3 - Data Description - 3-3 Measures of Position - Exercises 3-3 - Page 160: 17

Answer

a. $87$, $49$, $20$ b. 79 c. 75 d. 69

Work Step by Step

a. n=64, for x=78 there are 55 numbers below so the percentile=$\frac{55+0.5}{64}\times100\approx87$ for x=66 there are 31 numbers below so the percentile=$\frac{31+0.5}{64}\times100\approx49$ for x=59 there are 12 numbers below so the percentile=$\frac{12+0.5}{64}\times100\approx20$ b. 90th percentile, position $c=\frac{64\times 90}{100}\approx 58$ gives a value of 79 c. 80th percentile, position $c=\frac{64\times 80}{100}\approx 51$ gives a value of 75 d. 65th percentile, position $c=\frac{64\times 65}{100}\approx 42$ gives a value of 69
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