Introductory Statistics 9th Edition

Published by Wiley
ISBN 10: 1-11905-571-7
ISBN 13: 978-1-11905-571-6

Chapter 3 - Section 3.2 - Measures of Dispersion for Ungrouped Data - Exercises - Page 96: 3.32

Answer

Range = 25 Variance = 61.5 Standard Deviation = 7.8422

Work Step by Step

Range = Largest Value - Smallest Value = 16-(-9) = 25 Mean = [ 5 + (-7) + 2 + 0 + (-9) + 16 + 10 + 7 ] / 8 = 3 x=5, x-µ = 5-3=2 x=-7, x-µ= -7-3=-10 x= 2, x-µ= 2-3 = -1 x=0, x-µ= 0-3 = -3 x=-9, x-µ= -12 x=16, x-µ= 13 x=10,x-µ = 7 x=7,x-µ = 4 Variance =$[ 2^{2}+ (-10)^{2}+(-1)^{2}+(-3)^{2}+(-12)^{2}+13^{2}+7^{2}+4^{2} ]/ 8$ = (4 + 100 + 1 + 9 + 144 + 169+ 49+ 16)/8 =61.5 Standard Deviation = $\sqrt 61.5 = 7.8422$
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