Explanation Given: Consider the lists of expenditures (in billions of dollars) spent by states and local communities. State Education Public Welfare AL 10.4 6.6 AZ 9.7 9.1 CA 79.8 83.5 FL 25.1 24.4 GA 17.4 11.7 IL 17.7 21.2 MA 13.5 16.7 MD 12.0 10.8 MI 23.5 15.7 NJ 17.1 15.9 PA 22.9 24.3 TX 50.4 32.8 Calculation: To determine the five number summary that is the minimum value, lower quartile ( Q 1 ), median ( Q 2 ), upper quartile ( Q 3 ) and the maximum value of the distributions rewrite the expenditure of each states in ascending order. i 1 2 3 4 5 6 7 8 9 10 11 12 x i 9.7 10.4 12.0 13.5 17.1 17.4 17.7 22.9 23.5 25.1 50.4 79.8 Therefore the minimum and maximum values of the distributions are 9.7 and 79.8 respectively and the number of entry n = 12 . As, n 2 = 6 is an even number therefore the lower quartile will be: Q 1 = 1 2 { ( 0.25 n ) t h data + ( 0.25 n + 1 ) t h data } = 1 2 { 3 r d data + 4 t h data } = 1 2 ( 12.0 + 13.5 ) = 12.75 As the number of entry n = 12 is even number

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ISBN: 9780135335215

Author: Lial

Publisher: PEARSON

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Chapter 10.3, Problem 41E

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Chapter 10.3, Problem 40E

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