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## Errors and Uncertainties

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**Errors and Uncertainties**In Measurements and in Calculations**Types of Experimental Errors:**• Random Errors: • A result of variations in the performance of the instrument and/or the operator • Do NOT consistently occur throughout a lab • Some examples: • Vibrations or air currents when measuring mass • Inconsistent temperature (i.e. of the air) throughout a lab • Irregularities in object being measured (i.e. the wire is not the same thickness at all points along its length) • Human parallax error**Types of Experimental Errors:**• So what can be done about random errors? • Don’t rush through your measurements! Be careful! • Take as many trials as possible—the more trials you do, the less likely one odd result will impact your overall lab results**Types of Experimental Errors:**• Systematic Errors: • 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 • Some Examples: • Non-calibrated (or poorly calibrated) measuring tools • A “zero offset” on a measuring tool, requiring a “zero correction” • Instrument parallax error**Types of Experimental Errors:**• What can be done to reduce these? • Unfortunately, nothing…HOWEVER: • We can account for the systematic errors sometimes: • i.e. if there’s a zero offset, make sure all your data has been adjusted to account for that. • Recognizing systematic errors will impact the size of your absolute uncertainty (more details soon )**Are These “Errors”?**• Misreading the scale on a triple-beam balance • 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 • Miscalculations because you use the wrong equation**Are These “Errors”?**• NONE of these are experimental errors • They are MISTAKES • What’s the difference? • You need to check your work to make sure these mistakes don’t occur…ask questions if you need to (of your lab partner, me, etc.) • Do NOT put mistakes in your error discussion in the conclusion**Accuracy vs. Precision**• Accuracy: • How close a measured value is to the actual (true) value. • Precision: • Precision is how close the measured values are to each other.**Absolute Uncertainty**The length of the object being measured is obviously somewhere near 4·3cm (but it is certainly not exactly 4·3cm). The result could therefore be stated as 4·3cm ± half the smallest division on the ruler.**Absolute Uncertainty**Uncertainty Percentage uncertainty = X 100% Average value Consider a ruler: The uncertainty is +/- ½ a division It has an uncertainty of ±0.5mm Now consider the time taken for a ball to drop: