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Unformatted text preview: 9/22/11 1 Conservation of Energy Recap from last lecture: Energy due to gravity Equals (=) Loss of energy due to friction Plus (+) Remaining energy available to generate flow in pipe 15 ft 200 ft Heat Engineering 100:800 Numbers and Statistics Scientific Notation o Avogadros Number 602 213 670 000 000 000 000 000 6.0221367 x 10 23 0.60221367 x 10 24 Accuracy vs. Precision Random vs Systematic Error Random Error o Accurate, but lacks precision o Averages out o Fractional Uncertainty Uncertainty/Best Value Systematic Error o Precise, but lacks accuracy o Offset or Bias o Fractional Error Error/True Value SigniFcant igures Accurate digits not including zeros to the left to place decimal point: o 0.00342 o 342 o 340 Exact definitions have infinite sig figs (e.g. pi) Numbers in mathematical relationships have infinite sig figs (e.g. d=2r) Rounding o 0-4 down, 5-9 up o Round in last step of calculation Multiplication and Division: o Use same sig figs as least precise number Addition and Subtraction: o Align decimals and use least significant figure to the right 5.0 x 10.624 = 53.120 => 53 (2) (5) (2) 5.0 +14.697 19.697 => 19.7 9/22/11 2 Practice How many sig figs? 386.35 0.386 x 10 3 40.001 40.000 4.00 x 10 4 0.400 x 10 4 398,592 250 Statistics Used to characterize a population o Random sample o Representative of entire population Descriptive Statistics o Describes data Statistical Inference o Draw conclusions from data Histogram A way to represent large datasets visually Accumulate data in range bins o Select 10 to 20 to cover range of data Plot range vs. Number of points in range Demonstration Central Tendency Mean o Arithmetic mean of data series Median o Middle value of sorted data o Two middle values? then average them Mode o Value that appears most frequently in data set Outlier Effects x = 1 n x i i = 1 n " Demonstration Variance Range o Maximum value minimum value Deviation o Distance of a particular point from mean o Should sum to zero for entire data set How to get around zero sum o Absolute Value Mean Absolute Value o Square Standard Deviation Variance = square of standard deviation MD = 1 n x i " x i = 1 n # s = 1 n " 1 x i " x ( ) 2 i = 1 n # Examples Two examples with the same mean, but different standard deviation o Smal Standard Deviation 4,5,6,4,5,6,4,5,6,4,5,6 Mean: 5 Standard Deviation: 0.85 o Large Standard Deviation 20,-10,40,-30,100,-90,1245,-1235,72,-62,3,7 Mean: 5 Standard Deviation 531.3 9/22/11...
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- Fall '07