How Do You Calculate the Average Error in Measurements?

[lauralovesyou]

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?

 

[Mapes]

This may help: http://en.wikipedia.org/wiki/Propagation_of_uncertainty#Example_formulas"

 

[tomcue]

Hello,

Calculating average error involves finding the average of the measured values and then determining the error associated with that average. In your example, the average of the three landing distances would be (6.93 + 6.56 + 6.65)/3 = 6.71 cm. However, the error associated with this average would not simply be the sum of the individual errors (0.05 + 0.05 + 0.05 = 0.15 cm), as this would overestimate the true error. Instead, the error associated with the average is calculated using the standard error formula, which takes into account the number of measurements and their individual errors. In this case, the standard error would be 0.05 cm, resulting in an average of 6.71 cm +/- 0.05 cm. It is important to note that the error in the average is always reported to one significant figure, as you mentioned. I hope this helps clarify the process of calculating average error.