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1 Finding Percentiles Given: The ages, to the nearest year, of children at a Disney movie were: Find: a) P 30, the thirtieth percentile 3,7,15,8,4,6,11,10,7,5 b) P 72, the seventy second percentile

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2 The Formula - Part 1 The depth (or position from end) of a percentile requires the use of the formula nk 100 k is the desired percentile P k ( i.e., P 30 k = 30) n is the “sample size”, the number of data kn

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3 The Formula - Part 2 * “Integer” means calculation results in a whole number If when calculated does not result in an integer, then d(P k ) = next larger integer nk 100 (Do you have your sample data ready to use?) If when calculated results in an integer*, then d(P k ) = (that integer) + 0.5 nk 100

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4 Ranked data = { } The Procedure - Find P 30 Step 1: Rank the data (from smallest to largest) 3,4,5,6,7, 8,10,11, Sample data = { } 3, 7, 15, 8, 4, 6, 11, 10, 7, 5 15 Smallest 3 5th 7 Largest 15 7th 8 2nd 4 4th 6 9th 11 8th 10 6th 7 3rd 5 Step 2: Find for P 30 nk 100 nk 100 = (10) (30) 100 = 300 100 = 3 = 3 nk 100 Smallest5thLargest7th2nd4th9th8th6th3rd

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5 The Procedure (Continued) - Find P 30 Step 3: Determine the depth of P 30, d(P 30 ) Since and 3 is an integer, = 3, nk 100 d(P 30 ) = 3 + 0.5 = 3.5 That is, P 30 is in the 3.5 th position

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6 The Answer - P 30 Step 4: Find P 30 by locating the data in the 3.5th position of the ranked data Ranked data = { } 3,4,5,6,7, 8,10,11,15 1st2nd3rd4th 3.5th position = 11 2 = 5.5 + 2 = P 30 At most, 30% of the ages are below 5.5 years 56 6 6 5 5

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7 The Procedure - Find P 72 Step 1: The data was previously ranked: Sample data = { } 3, 7, 15, 8, 4, 6, 11, 10, 7, 5 Ranked data = { } 3,4,5,6,7, 8,10,11,15 Step 2: Find for P 72 nk 100 nk 100 = (10) (72) 100 = 720 100 = 7.2 = 7.2 nk 100

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8 Step 3: Determine the depth of P 72, d(P 72 ) Since, and 7.2 is not an integer, = 7.2 nk 100 d(P 72 ) = 8 (next integer larger than 7.2) That is, P 72 is in the 8 th position The Procedure (Continued) - Find P 72

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9 The Answer - P 72 Step 4: Find P 72 by locating the data in the 8th position of the ranked data Ranked data = { } 3,4,5,6,7, 8,10,11,15 1st2nd3rd4th 8th position P 72 = At most, 72% of the ages are below 10 years 5th6th7th8th 10

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Understanding the Result Percentiles are a measure of position within a set of data. They provide information on the relative standing of a person or object with respect to the sample taken. If P 30 =5.5, then at most, 30% of the ages are below 5.5 years AND at most, 70% of the ages are above 5.5 years * Common mistake: Forgetting to sort the data * If P 72 =10, then at most, 72% of the ages are below 10 years AND at most, 28% of the ages are above 10 years

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Copyright © Cengage Learning. All rights reserved. 2 Descriptive Analysis and Presentation of Single-Variable Data.

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