1 CHAPTER 17 17 1 The data can be tabulated as i 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 y 8 8 9 4 10 9 8 10 1 9 5 10 1 10 4 9 5 9 5 9 8 9 2 7 9 8 9 9 6 9 4 11 3 10 4 8 8 10 2 10 9 4 9 8 10 6 8 9 241 3 a y yi y 2 0 7259 0 0635 0 1211 0 0219 0 2007 0 0231 0 2007 0 5595 0 0231 0 0231 0 0219 0 2043 3 0695 0 5655 0 0027 0 0635 2 7159 0 5595 0 7259 0 3003 0 1211 0 0635 0 0219 0 8987 0 5655 11 8624 241 3 9 652 25 b s y 11 8624 0 703041 25 1 c s 2y 0 7030412 0 494267 0 703041 100 7 28 9 652 e t0 05 2 25 1 2 063899 0 703041 L 9 652 2 063899 9 361799 25 0 703041 U 9 652 2 063899 9 942201 25 f The data can be sorted and then grouped We assume that if a number falls on the border between bins it is placed in the lower bin d c v lower 7 5 8 8 5 9 9 5 upper 8 8 5 9 9 5 10 Frequency 1 0 4 7 6 PROPRIETARY MATERIAL The McGraw Hill Companies Inc All rights reserved No part of this Manual may be displayed reproduced or distributed in any form or by any means without the prior written permission of the publisher or used beyond the limited distribution to teachers and educators permitted by McGraw Hill for their individual course preparation If you are a student using this Manual you are using it without permission 2 10 10 5 11 10 5 11 11 5 5 1 1 Frequency The histogram can then be constructed as 8 7 6 5 4 3 2 1 0 7 75 8 25 8 75 8 5 8 5 8 5 7 5 7 833 Bin 17 2 The data can be sorted in ascending order and tabulated as i y 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 28 15 28 55 28 65 28 75 29 05 29 15 29 25 29 25 29 35 29 35 29 45 29 65 29 65 29 65 29 65 29 75 29 75 29 85 30 15 30 15 30 25 30 45 30 45 30 55 30 65 30 85 31 25 33 65 835 3 yi y 2 2 829605 1 64389 1 397462 1 171033 0 611747 0 465319 0 33889 0 33889 0 232462 0 232462 0 146033 0 033176 0 033176 0 033176 0 033176 0 006747 0 006747 0 000319 0 101033 0 101033 0 174605 0 381747 0 381747 0 515319 0 66889 1 036033 2 010319 14 57603 29 50107 835 3 29 83214 28 b median 29 65 c mode 29 65 d range maximum minimum 33 65 28 15 5 5 a y PROPRIETARY MATERIAL The McGraw Hill Companies Inc All rights reserved No part of this Manual may be displayed reproduced or distributed in any form or by any means without the prior written permission of the publisher or used beyond the limited distribution to teachers and educators permitted by McGraw Hill for their individual course preparation If you are a student using this Manual you are using it without permission 3 e s y 29 50107 1 045291 28 1 f s 2y 1 0452912 1 092632 1 045291 100 3 50 29 83214 h The data can be sorted and grouped g c v Lower 28 28 4 28 8 29 2 29 6 30 30 4 30 8 31 2 31 6 32 32 4 32 8 33 2 33 6 Upper 28 4 28 8 29 2 29 6 30 30 4 30 8 31 2 31 6 32 32 4 32 8 33 2 33 6 34 Midpoint Frequency 28 2 1 28 6 3 29 2 29 4 5 29 8 7 30 2 3 30 6 4 31 1 31 4 1 31 8 32 2 32 6 33 33 4 33 8 1 The histogram can then be constructed as 8 7 6 5 4 3 2 1 4 8 33 33 33 2 8 4 6 32 32 31 31 31 2 8 4 6 30 30 29 29 29 6 28 28 2 0 i 68 of the readings should fall between y s y and y s y That is between 29 83214 1 04529 28 78685 and 29 83214 1 04529 30 87743 Twenty two values fall between these bounds which is equal to 22 28 78 6 of the values which is somewhat higher than the expected value of 68 for the normal distribution Here is a script showing how the problem would be answered using MATLAB s built in functions clear clf clc format compact y 29 65 28 55 28 65 30 15 29 35 29 75 29 25 30 65 28 15 29 85 29 05 30 25 30 85 28 75 29 65 30 45 29 15 30 45 33 65 29 35 29 75 31 25 29 45 30 15 29 65 30 55 29 65 29 25 meany mean y mediany median y modey mode y range max y min y stddevy std y PROPRIETARY MATERIAL The McGraw Hill Companies Inc All rights reserved No part of this Manual may be displayed reproduced or distributed in any form or by any means without the prior written permission of the publisher or used beyond the limited distribution to teachers and educators permitted by McGraw Hill for their individual course preparation If you are a student using this Manual you are using it without permission 4 variancey var y cv stddevy meany ny 34 28 0 4 1 binmids linspace 28 0 4 34 0 4 ny hist y binmids meany 29 8321 mediany 29 6500 modey 29 6500 range 5 5000 stddevy 1 0453 variancey 1 0926 cv 0 0350 7 6 5 4 3 2 1 0 28 29 30 31 32 33 34 17 3 The results can be summarized as y versus x y 4 851535 0 35247x 1 06501 0 914767 Best fit equation Standard error Correlation coefficient x versus y x 9 96763 2 374101y 2 764026 0 914767 We can also plot both lines on the same graph y 12 8 y y versus x x versus y 4 0 0 5 10 15 x 20 Thus the best fit lines and the standard errors differ This makes sense because different errors are being minimized depending on our choice of the dependent ordinate and independent abscissa variables In contrast the correlation coefficients are identical since the same amount of uncertainty …
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