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Lecture 27 - Simple Statistics Measurement of the...

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Simple Statistics Measurement of the coefficient of thermal expansion of structural steel [ × 10 - 6 in/(in ⋅ ° F)] 535 6 667 6 670 6 592 6 633 6 627 6 598 6 499 6 621 6 445 6 451 6 403 6 703 6 542 6 659 6 624 6 733 6 662 6 721 6 396 6 564 6 435 6 625 6 555 6 655 6 478 6 621 6 543 6 399 6 552 6 667 6 325 6 495 6 775 6 554 6 485 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Mean, standard deviation, variance, etc.
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Statistics Review Arithmetic mean Standard deviation about the mean Variance (spread) Coefficient of variation (c.v.) ( 29 2 i t t y y y S 1 n S s - = - = ; ( 29 ( 29 1 n n y y 1 n y y s 2 i 2 i 2 i 2 y - - = - - = / % . . 100 y s v c y × =
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1 6.485 0.007173 42.055 2 6.554 0.000246 42.955 3 6.775 0.042150 45.901 4 6.495 0.005579 42.185 5 6.325 0.059875 40.006 6 6.667 0.009468 44.449 7 6.552 0.000313 42.929 8 6.399 0.029137 40.947 9 6.543 0.000713 42.811 10 6.621 0.002632 43.838 11 6.478 0.008408 41.964 12 6.655 0.007277 44.289 13 6.555 0.000216 42.968 14 6.625 0.003059 43.891 15 6.435 0.018143 41.409 16 6.564 0.000032 43.086 17 6.396 0.030170 40.909 18 6.721 0.022893 45.172 19 6.662 0.008520 44.382 20 6.733 0.026669 45.333 21 6.624 0.002949 43.877 22 6.659 0.007975 44.342 23 6.542 0.000767 42.798 24 6.703 0.017770 44.930 25 6.403 0.027787 40.998 26 6.451 0.014088 41.615 27 6.445 0.015549 41.538 28 6.621 0.002632 43.838 29 6.499 0.004998 42.237 30 6.598 0.000801 43.534 31 6.627 0.003284 43.917 32 6.633 0.004008 43.997 33 6.592 0.000498 43.454 34 6.670 0.010061 44.489 35 6.667 0.009468 44.449 36 6.535 0.001204 42.706 236.509 0.406514 1554.198 ( 29 2 i 2 i i y y y y i - Ave=6.5697 n y y i =
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Coefficient of Thermal Expansion ( 29 ( 29 % . % . . % . . . . / ) . ( . / . . . . . 64 1 100 5697 6 10777 0 100 y s v c 0116147 0 35 406514 0 35 36 509 236 198 1554 1 n n y y s 10777 0 1 36 406514 0 1 n S s 406514 0 y y S 5697 6 36 509 236 n y y y 2 2 i 2 i 2 y t y 2 i t i = × = × = = = - = - - = = - = - = = - = = = =
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