Uncertainty in Measurement Accuracy and Precision.

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Presentation transcript:

Uncertainty in Measurement Accuracy and Precision

How would you describe the appearance of a criminal to a police officer??

Measurement Uncertainty Some error or uncertainty always exists in any measurement. The amount of uncertainty depends both upon the skill of the measurer and upon the quality of the measuring tool.

Accuracy How close the measurements are to the true value Depends on the instrument that you area using to measure.

Precision How close measurements are to each other; these measurements are not necessarily close to the true value. Precision is the smallest degree which can be measured by a tool.

Kami measured the volume of a liquid three times and got these results: mL, mL, mL. The actual volume of the liquid is mL. Are Kami’s measurements precise? Are they accurate?

Accuracy vs. Precision re:

In basketball, the basket is only 18 inches across and the ball is a little less than 10 inches in diameter. There’s not much room for error!!! Does the shot need to be accurate or precise for the ball to make it into the basket?? Re:

Errors in Measurement Error? No... you didn't measure it wrong... this is about accuracy. Accuracy is mathematically expressed as error. Measuring instruments are not exact!

Degree of Accuracy Accuracy depends on the instrument you are using, but as a general rule: The degree of accuracy is half a unit each side of the unit of measure.

Examples re: mathisfun.com When your instrument measures in "1"s then any value between 6½ and 7½ is measured as "7" When your instrument measures in "2"s then any value between 7 and 9 is measured as "8"

Plus or Minus We can show the error using the "Plus or Minus" sign:

Plus or Minus re: mathisfun.com When the value could be between 6½ and 7½, the error is Value is When the value could be between 7 and 9, the error is + 1 Value is 8 + 1

Absolute Error Absolute Error (AE) is the difference between the actual and measured value (how different your value is from the accepted value). AE = Your value – Accepted value

Relative Error The Relative Error is the Absolute Error divided by the actual measurement. We don't know the actual measurement, so the best we can do is use the measured value: Relative Error = Absolute Error Measured Value

Example The length of a fence is m long So: Absolute Error = 0.05 m And: Relative Error = 0.05 m = m And: Percentage Error = 0.4%

Deviation Precision is mathematically expressed as deviation. Absolute deviation (AD) is how different a value is from the average value. AD = Your value – Average value Relative deviation (RD) is the percentage difference between a value and the average. RD = (AD ÷ average) x 100

Deviation Precision is mathematically expressed as deviation. The Deviation is a measure of how spread out numbers are