1. calculate the median and mean of the justice's years of service2. what proportion of the justices have served for longer than the mean service length? As of January 2010, the nine justices of the U.S. Supreme Court and their years ofappointmentand services are as follows:JusticeStevensScaliaKennedyThomasGinsbergBreyerRobertsAlitoSotomayorYearAppointed197519861988199119931994200520062009Years ofService342321181615430

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College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter8: Sequences, Series, And Probability

Section8.CT: Chapter Test

Problem 16CT: How many six-digit license plates can be made if no plate begins with 0 or 1?

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1. calculate the median and mean of the justice's years of service

2. what proportion of the justices have served for longer than the mean service length?

As of January 2010, the nine justices of the U.S. Supreme Court and their years of
appointment
and services are as follows:
Justice
Stevens
Scalia
Kennedy
Thomas
Ginsberg
Breyer
Roberts
Alito
Sotomayor
Year
Appointed
1975
1986
1988
1991
1993
1994
2005
2006
2009
Years of
Service
34
23
21
18
16
15
4
3
0

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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