126 Chapter 3 Numerical Summaries of Data Procedure for Computing the Data Value Corresponding to a Given Percentile Step 1: Arrange the data in increasing order. Step 2: Let n be the number of values in the data set. For the pth percentile, compute the value L = p 100 · n Step 3: If L is a whole number, then the pth percentile is the average of the number in position L and the number in position L + 1. If L is not a whole number, round it up to the next higher whole number. The pth percentile is the number in the position corresponding to the rounded-up value. EXAMPLE 3.23 Computing a percentile CAUTION Always round L up. Do not round down. Compute the 30th percentile of the Los Angeles rainfall data. Solution Step 1: Table 3.10 presents the data in increasing order. Step 2: There are n = 42 values in the data set. For the 30th percentile, we take p = 30 and compute L = 30 100 · 42 = 12.6 Step 3: Since L = 12.6 is not a whole number, we round it up to 13. The 30th percentile is the number in the 13th position. From Table 3.10 we can see that the 30th percentile is 1.22. Table 3.10 Annual Rainfall in Los Angeles During February, in Increasing Order Year Rainfall Year Rainfall Year Rainfall Year Rainfall 1984 0.00 1982 0.70 1990 3.12 1993 6.61 1997 0.08 1987 1.22 1994 3.21 1973 7.89 1967 0.11 1995 1.30 1975 3.54 1992 7.96 1972 0.13 1981 1.48 1976 3.71 1969 8.03 1974 0.14 1966 1.51 1991 4.13 2001 8.87 1977 0.17 1988 1.72 1983 4.37 1978 8.91 1965 0.23 1989 1.90 2003 4.64 2005 11.02 2002 0.29 2006 2.37 2004 4.89 1980 12.75 1968 0.49 1970 2.58 1996 4.94 1998 13.68 1999 0.56 1985 2.84 2000 5.54 1971 0.67 1979 3.06 1986 6.10 Computing the percentile corresponding to a given data value Sometimes we are given a value from a data set, and wish to compute the percentile corresponding to that value. Following is a simple procedure for doing this.
navidi_monk_essential_statistics_1e_ch1_3
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