Statistics: Informed Decisions Using Data (4th Edition)

Published by Pearson
ISBN 10: 0321757270
ISBN 13: 978-0-32175-727-2

Chapter 3 - Section 3.3 - Assess Your Understanding - Applying the Concepts - Page 164: 14a

Answer

$μ=25.49~years$ $σ=5.44~years$

Work Step by Step

$x_1=First~Class~Midpoint=12.5$ $x_2=Second~Class~Midpoint=17.5$ $x_3=Third~Class~Midpoint=22.5$ $x_4=Fourth~Class~Midpoint=27.5$ $x_5=Fifth~Class~Midpoint=32.5$ $x_6=Sixth~Class~Midpoint=37.5$ $x_7=Seventh~Class~Midpoint=42.5$ $x_8=Eighth~Class~Midpoint=47.5$ $μ=\frac{Σx_if_i}{Σf_i}=\frac{12.5\times9.8+17.5\times551.9+22.5\times1226.4+27.5\times1108.2+32.5\times549.9+37.5\times140.7+42.5\times23.2+47.5\times1.1}{3611.2}=25.49$ $σ=\sqrt {\frac{(x_i-μ)^2f_i}{Σf_i}}=\sqrt {\frac{(12.5-25.49)^2\times9.8+(17.5-25.49)^2\times551.9+(22.5-25.49)^2\times1226.4+(27.5-25.49)^2\times1108.2+(32.5-25.49)^2\times549.9+(37.5-25.49)^2\times140.7+(42.5-25.49)^2\times23.2+(47.5-25.49)^2\times1.1}{3611.2}}=5.44$
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