Percentage uncertainty and percentage error

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SUMMARY

The discussion focuses on calculating percentage uncertainty and percentage error using recorded measurements. The user presents a set of diameter measurements (11.67, 12.67, 13.9, 12.67, 12.67, 12.66 mm) and seeks to determine the percentage error in the average diameter. Additionally, the user records values for x (12.8 cm), y (30.2 cm), and T (2.2 N) to find the percentage uncertainty in y. The correct formula for percentage uncertainty is clarified as the absolute uncertainty divided by the measured value, expressed as a percentage.

PREREQUISITES
  • Understanding of basic statistical concepts, including average and error calculations.
  • Familiarity with the formula for percentage uncertainty: (absolute uncertainty / measured value) × 100.
  • Knowledge of how to record and interpret measurement data accurately.
  • Basic proficiency in using measurement tools such as rulers and Newton meters.
NEXT STEPS
  • Study the concept of absolute uncertainty and how it applies to various measurements.
  • Learn how to calculate average values and their associated errors in experimental data.
  • Research the differences between percentage error and percentage uncertainty in scientific measurements.
  • Explore practical examples of calculating percentage uncertainty in physics experiments.
USEFUL FOR

Students in physics or engineering, educators teaching measurement techniques, and anyone involved in experimental data analysis who needs to understand percentage uncertainty and error calculations.

david18
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You record the following data Diameter/mm: 11.67, 12.67, 13.9, 12.67, 12.67, 12.66 You take the average of these values to be the diameter, but what is the percentage error in this value?

I tried working this problem out but I can't use the normal formula as it is spread over many values and there is no accepted value. I got some numbers; 17.55%, 1.5% but theyr all wrong.


W = T(x+y)/x

Where W is the weight of the stand and T is the Newton meter reading.

You measure and record the values of x, y (with a ruler) and T. The following data is recorded:

x = 12.8 cm , y = 30.2 cm, T= 2.2 N

What is the percentage uncertainty in y?

This one wants the percentage uncertainty which I'm unsure of how to find. I did try 30.25(max value) - 30.15(lowest value) / 2 = 0.05 and find it as a percentage but it turned out to be wrong...



Any help with these problems would be much appreciated.
 
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Percentage Uncertainty

Uncertainties may be quoted as a percentage rather than absolute values. An uncertainty of 124 (+ or -) 1 means 1 in 124 ie.

Percentage Uncertainty = \frac{1}{124}\times100 = 0,08
 

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