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# Applied Statistics with Computers MATH 254

BSU

GPA 3.72

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This 2 page Class Notes was uploaded by Breanne Schaden PhD on Saturday October 3, 2015. The Class Notes belongs to MATH 254 at Boise State University taught by Mary Kersey in Fall. Since its upload, it has received 12 views. For similar materials see /class/217997/math-254-boise-state-university in Mathematics (M) at Boise State University.

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Date Created: 10/03/15

Basics of Linear Transformation 1 Linear Transformation 0 De nition Suppose that x17x277xn is given data Then we transform it into 34173427 7 gm using y a 9337 where a and b are constants Example 1 The following data denote the study times hour day of four students of MATH 254 class 327 437 507 72 Then we could change the unit of datahour into minutes using ymm 60 X Xhom Then the transformed data are 1927 2587 3007 432 Example 2 The following data denote the temperaturesdegree Fahrenheit of Boise during last 3 days 327 377 42 5 Let s change the unit into Celsiusor Centigrade using yo g X XF 32 Then the transformed data are 07 287 56 2 Statistical property of linear transform Suppose that we transform original data 317 327 7 3377 into y17 y27 7 yn using y a 3 where a and b are constants Also let X and S be the mean and variance of the original data7 respectively Then 0 The mean and variance of the transformed data y17 y27 7 yn7 l7 and 332 are Y a b X 21 and 832 b2 S 22 1 Example 3 In Example 17 X 4925 and S 2849 Since I 607 from 21 and 227 l7 60 X X 60 X 4925 2955 and 832 602 x S2 602 x 2849 102564 Calculate the mean and variance of the transformed data directly and make sure that they are same as the above In y a 9337 the intercept 1 changes the origin and the slope I does the unit of original data Linear transformations do not change the shape of a distribution For ex ample7 if the original data2 s is skewed to the rightthe left then the transformed data is also skewed to the right the left However7 the mea sure of center and variability will be changed Example 4 Mary and John both measure the weights of the same ve newly hatched pythons Mary measures them in ounces and John uses gram Assume that 1 ounce2835 grams The followings are Mary s measurements in ounces 113 102 123 106 116 A Find the equation for linear transformation between ounce and gram B Calculate Mary s mean X MW and variance 312V my C Using the results in A and B7 calculate the John s mean onhn and variance 33 ohn

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