Error Analysis Monday, August 17 th

Do Now  Complete the following calculation. Make sure you use the correct amount of sig figs:  x174.5  Once you get your answer, put it into scientific notation

Accuracy and Precision AccuracyPrecision How close you are to the actual value Example: The density of water is 1 g/mL. You are accurate if your experimental value is close to 1 (0.99, 1.01) How close your measurements are to one another Precision refers to the reproducibility of the measurement and exactness of description in a number

Accuracy vs. Precision Accuracy= bulls eye (or average out to bulls eye) Precision = darts are close together

Precision  To decide on precision, you need several measurements (notice multiple arrow holes), and you do not need to know the true value (none of the values are close to the target but all the holes are close together.)

 A sample is known to weigh g. Jane weighed the sample five different times with the resulting data. Which measurement was the most accurate?  g  g  g  g

Mark each set of numbers as having a high or low accuracy and precision. Object measured is 50 cm length  52  60  48  41

Mark each set of numbers as having a high or low accuracy and precision. Object measured is 15 cm 2 area     13.22

Mark each set of numbers as having a high or low accuracy and precision. Object measured is 32 g mass  40  55  32  50

Mark each set of numbers as having a high or low accuracy and precision. Object measured is 0.31 g/cm 3 density  0.30  0.32  0.31

Expressing Errors in Measurement  Scientists often express their uncertainty and error in measurements by giving a percent error. The percent error is defined as: *NOTICE, this is not percent yield

Expressing Errors in Measurement

Error Analysis in Chemistry  There are two sources of error in chemistry labs: 1. Systematic Errors (determinate) 2. Random Errors (indeterminate)

Systematic Errors  Errors due to identifiable causes  Likely to give results that are consistently too high or too low  Sources of error can usually be identified  Affects accuracy  Examples  Equipment being consistently wrongly used by experimenter  Wrongly calibrated machine

Random Errors  Sources or error cannot always be identified  The random error is equivalent to the uncertainty in measurement.  Affects precision  Due to the precision limitations of the measurement device. Random errors usually result from the experimenter's inability to take the same measurement in exactly the same way to get exact the same number

How to Minimize Error  Random: take more data. Random error can be reduced by averaging over a large number of observations.  Systematic: Be sure your instruments are properly calibrated. (These are harder to detect)

Reporting Data  The mean: or average value. Defined as the sum of all of the values, divided by the number of measurements.

Find the Mean