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 162: 3

Answer

$x̅=70.6~°F$ $s=3.5~°F$

Work Step by Step

$x_1=$ First Class Midpoint = 63 $x_2=$ Second Class Midpoint = 66.5 $x_3=$ Third Class Midpoint = 69 $x_4=70$ $x_5=$ Fifth Class Midpoint = 72 $x_6=$ Sixth Class Midpoint = 75 $x_7=$ Seventh Class Midpoint = 79 $x̅=\frac{Σx_if_i}{Σf_i}=\frac{63\times31+66.5\times67+69\times198+70\times195+72\times120+75\times89+79\times50}{750}=70.6$ $s=\sqrt {\frac{Σ(x_i-x̅)^2f_i}{(Σf_i)-1}}=\sqrt {\frac{(63-70.65)^2\times31+(66.5-70.65)^2\times67+(69-70.65)^2\times198+(70-70.65)^2\times195+(72-70.65)^2\times120+(75-70.65)^2\times89+(79-70.65)^2\times50}{750-1}}=3.5$
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