12_lecturedatareduction1

# 12_lecturedatareduction1 - Data Reduction Its Poetic 16.621...

This preview shows pages 1–13. Sign up to view the full content.

Data Reduction “It’s Poetic” 16.621 March 18, 2003

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Introduction A primary goal of your efforts in this course will be to gather empirical data so as to prove (or disprove) your hypothesis Typically the data that you gather will not directly satisfy this goal Rather, it will be necessary to “reduce” the data, to put it into an appropriate form, so that you can draw valid conclusions • In our discussion today we will examine some typical methods for processing empirical data Caution-garbage in/garbage out still applies
Hiawatha Designs an Experiment by Maurice G. Kendall From The American Statistician Vol. 13, No. 5, 1959, pp 23-24 Verses 1 through 6

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Deyst’s 16.62X Project I have performed a very simple experiment The hypothesis was: my driving route distance, from West Garage to my driveway in Arlington, is eight miles On a number of trips I recorded the mileage, as indicated by the odometer of my automobile I now wish to reduce the data and draw some conclusions
Experimental Project (cont.) My experimental procedure was: at the exit from West Garage I zeroed my trip odometer and when I reached my driveway at home I recorded the odometer reading On each of ten trips I took the same route home

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Error Sources Random errors Odometer readout resolution Odometer mechanical variations Route path variations Tire slippage Systematic errors Bias in the odometer readings Odometer scale factor error Tire diameter decreases due to wear
Error Sources (cont.) The resolution I achieved in reading the odometer was within ± .025 miles The best knowledge I have about the other random errors is that they were all in the range of ± .10 miles I zeroed the odometer at the beginning of each trip so any bias in the measurements is small (i.e. about ± .005 miles)

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Error Sources (cont.) I did a scale factor calibration by driving 28 miles, according to mileage markers on Interstate 95, and in both directions I recorded 27.425 miles on my odometer Thus, the scale factor is 27.425 odometer indicted miles S . F . = = .980 28 actual miles And any error in the scale factor due to readout resolution is .025 ≅± .0006 e SF 2 28
Recorded Data Trip Number Mileage Reading S.F. Corrected Mileage reading 1 7.825 7.985 2 7.850 8.010 3 7.875 8.036 4 7.900 8.061 5 7.850 8.010 6 7.825 7.985 7 7.875 8.036 8 7.850 8.010 9 7.875 8.036 10 7.825 7.985

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Mileage Data Analysis My system model is that the route distance is constant To minimize the effect of random errors take the sample mean (average) of the data to obtain an estimate n d ˆ = 1 d i = 8.015 miles n i = 1
Mileage Data Analysis (cont.) Variations of the individual measurements, about this estimate are e i = d i d ˆ The sample mean of these variations is n n 1 n e ˆ = e i = 1 ( d i d ˆ ) = 0 i = 1 n i = 1 So the estimate is unbiased

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Mileage Data Analysis (cont.)
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 11/08/2011 for the course AERO 16.61 taught by Professor Earlmurman during the Spring '03 term at MIT.

### Page1 / 41

12_lecturedatareduction1 - Data Reduction Its Poetic 16.621...

This preview shows document pages 1 - 13. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online