How Do You Calculate the Average Error in Measurements?

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SUMMARY

The average error in measurements is calculated by first determining the mean of the measured values and then calculating the combined uncertainty. In the provided example, the average distance is 6.71 cm, and the uncertainty should be reported as +/- 0.05 cm, reflecting the precision of the individual measurements. The correct approach is to average the distances and retain the smallest uncertainty from the individual measurements, resulting in 6.71 cm +/- 0.05 cm. This method aligns with the principles of uncertainty propagation as outlined in the Wikipedia article on the topic.

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lauralovesyou
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Hi,

I was just wondering how you calculate the average error, is there a certain formula?

Ex:

Three landing distances were measured and they were

6.93 cm +/- 0.05cm
6.56 cm +/- 0.05cm
6.65 cm +/- 0.05cm

To calculate error, do you add the landing distances then divide them by three and then add the errors for each one, therefore the average would be 6.71cm +/- 0.2cm (actual is 0.15cm however error is always in one significant figure) or do you divide the averages by three also, therefore get 6.71cm +/- 0.05cm?
 
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