Elementary Statistics (12th Edition)

Published by Pearson
ISBN 10: 0321836960
ISBN 13: 978-0-32183-696-0

Chapter 3 - Statistics for Describing, Exploring, and Comparing Data - 3-3 Measures of Variation - Basic Skills and Concepts - Page 106: 2


a) True. b)True. c) False. d)True. e)False.

Work Step by Step

Standard deviation: $\sqrt{\frac{\sum(x-\mu)^2}{n}}.$ a)Mean:$\mu=\frac{\sum x}{n}=\frac{25\cdot20}{25}=20$ Hence all $x-\mu=0$, hence the standard deviation is 0, hence the statement is true. b) True, because in the formula of standard deviation, all values are non-negative, hence it cannot be less than 0. c) $Variance=(standard \ deviation)^2=(3 \ kg)^2=9 \ kg^2\ne9 \ kg$, hence the statement is false. d) $standard \ deviation=\sqrt{variance}=\sqrt{16 \ sec^2}= 4 \ sec.$ Hence the statement is true. e)$Variance=(standard \ deviation)^2=(25 \ cm)^2=625 \ cm^2\ne5 \ cm^2$, hence the statement is false.
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