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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 Avogadro’s 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 zero’s 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 04 down, 59 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
 Winarsky/Hildinger
 Thermodynamics, Energy, Heat, Heat Transfer, • Standard deviation

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