Errors and Uncertainties In Measurements and in Calculations.

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Presentation transcript:

Errors and Uncertainties In Measurements and in Calculations

Are These “Errors”? Misreading the scale on a triple-beam balance Misreading the scale on a triple-beam balance Incorrectly transferring data from your rough data table to the final, typed, version in your report Incorrectly transferring data from your rough data table to the final, typed, version in your report Miscalculating results because you did not convert to the correct fundamental units Miscalculating results because you did not convert to the correct fundamental units Miscalculations because you use the wrong equation Miscalculations because you use the wrong equation

Are These “Errors”? NONE of these are experimental errors NONE of these are experimental errors They are MISTAKES They are MISTAKES What’s the difference? What’s the difference? Mistakes are math errors, reading errors, and the like that occur because you’re rushing or not performing the lab as expected. Mistakes are math errors, reading errors, and the like that occur because you’re rushing or not performing the lab as expected. Fixing a mistake would improve YOUR results only. Fixing a mistake would improve YOUR results only. Errors are inherent qualities of the lab setup, equipment or usage. Errors are inherent qualities of the lab setup, equipment or usage. Fixing an error would improve EVERYONE’S results, not just your own. Fixing an error would improve EVERYONE’S results, not just your own.

Types of Experimental Errors: Random Errors: Random Errors: A result of variations in the performance of the instrument and/or the operator A result of variations in the performance of the instrument and/or the operator Do NOT consistently occur throughout a lab Do NOT consistently occur throughout a lab Systematic Errors: Systematic Errors: Errors that are inherent to the system or the measuring instrument Errors that are inherent to the system or the measuring instrument Results in a set of data to be centered around a value that is different than the accepted value Results in a set of data to be centered around a value that is different than the accepted value

Accuracy vs. Precision Accuracy: Accuracy: How close a measured value is to the actual (true) value. How close a measured value is to the actual (true) value. Precision: Precision: Precision is how close the measured values are to each other. Precision is how close the measured values are to each other.

Accuracy vs. Precision

Measuring in Astronomy When I record a measurement in science, I write down all of the numbers I’m sure of – PLUS one estimated place. When I record a measurement in science, I write down all of the numbers I’m sure of – PLUS one estimated place. Example: Example: I’m certain of: 4.9 cm (not quite to 5 yet) I’m certain of: 4.9 cm (not quite to 5 yet) I estimate: It reached 3/10ths of the space between markings I estimate: It reached 3/10ths of the space between markings My measurement is recorded as: 4.93 cm My measurement is recorded as: 4.93 cm

Absolute Uncertainty The smallest uncertainty in a measurement is ± half the smallest division The smallest uncertainty in a measurement is ± half the smallest division Example: Example: I’m certain of: 2.3 cm I’m certain of: 2.3 cm I estimate: 2/10ths of the space between markings I estimate: 2/10ths of the space between markings ½ the smallest division: 0.05 cm ½ the smallest division: 0.05 cm My measurement is recorded as: 2.32 ± 0.05 cm My measurement is recorded as: 2.32 ± 0.05 cm 8