This preview shows pages 1–3. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
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 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...
View Full
Document
 Fall '07
 Winarsky/Hildinger

Click to edit the document details