# 17 1 percentiles quartiles for a sorted list of

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Percentiles & QuartilesFor a sorted list of values,thek-th Percentileof a sorted list of values, denoted byPk, is a numbersuch thatk%of values are less and(100-k)%are larger than it;thequartilesareQ1=P25.Q2=Median=P50.Q3=P75.These divide a ranked list of values into four equal parts, each onecontains about 25% of the values.Finding the Percentile of a Data ValuePercentile of value ofx=number of values less thanxtotal number of values.100(Round the result to nearest whole number).A. Bourhim (Syracuse University)Measures of CenterMAT121, Spring 201518 / 1
ExampleSorted movie budget amounts (in millions of dollars) of a sample of moviesare given:4.556.57202029303540404150526065686870Find the percentiles of29and60.
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How to find the PercentilePk(see the chart page 116)To findPk:1Arrange the list in an increasing order.2Find the so-called locatorL=k100.nand see if it is a whole number or not. Here,nis the total number of datavalues (sample size).3ifLis not a whole number, then round it up to the next whole number andPk=Lthvalue,from the ranked list.4ifLis a whole number, thenPk=Lthvalue+(L+1)thvalue2.These values should be taken from the ranked list.A. Bourhim (Syracuse University)Measures of CenterMAT121, Spring 201520 / 1
ExampleReconsider the previous example4.556.57202029303540404150526065686870and findP40,P67,Q1, andQ3.A. Bourhim (Syracuse University)Measures of CenterMAT121, Spring 201521 / 1
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