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Let x = (x₁,...,xn) be a data set, and denote its sample standard deviation with sx. Let y₁ = ax; + b. (a) Show that sy = |a|sx, where sy is the sample standard deviation of y = (y₁,..., yn). (b) Show that Median(y) = a · Median(x) + b. (c) If a > 0, can you write the relation between Q1(y) and Q1(x)? What happens if a < 0? Note: Q1(x) (or Q1(y)) denotes the first quartile of the distribution of the random variable x (or y)

Let x = (x₁,...,xn) be a data set, and denote its sample standard deviation with sx. Let y₁ = ax; + b. (a) Show that sy = |a|sx, where sy is the sample standard deviation of y = (y₁,..., yn). (b) Show that Median(y) = a · Median(x) + b. (c) If a > 0, can you write the relation between Q1(y) and Q1(x)? What happens if a < 0? Note: Q1(x) (or Q1(y)) denotes the first quartile of the distribution of the random variable x (or y)

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.5: Comparing Sets Of Data
Problem 14PPS
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(x₁,...,xn) be a data set, and denote its sample standard deviation with s. Let yį = ax; + b. (a) Show that sy = |a|sx, where sy is the sample standard deviation of y = (y₁,..., Yn). (b) Show that Median(y) = a. Median(x) + b. Let x = (c) If a > 0, can you write the relation between Q1(y) and Q1(x)? What happens if a < 0? Note: Q1(x) (or Q1(y)) denotes the first quartile of the distribution of the random variable x (or y)
Transcribed Image Text:(x₁,...,xn) be a data set, and denote its sample standard deviation with s. Let yį = ax; + b. (a) Show that sy = |a|sx, where sy is the sample standard deviation of y = (y₁,..., Yn). (b) Show that Median(y) = a. Median(x) + b. Let x = (c) If a > 0, can you write the relation between Q1(y) and Q1(x)? What happens if a < 0? Note: Q1(x) (or Q1(y)) denotes the first quartile of the distribution of the random variable x (or y)
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