3 ms·
As a general rule, sampling a normal distribution N times decreases the uncertainty by a multiple of 1/sqrt(N). For instance, to know the mean of an unknown dis
by LegionMammal978 5y ago
As a general rule, sampling a normal distribution N times decreases the uncertainty by a multiple of 1/sqrt(N). For instance, to know the mean of an unknown distribution to within N digits, the number of observations must be on the order of 2N digits long. I learned this the hard way when attempting some statistical experiments; it may answer your question here.
- amelius 5y agoHow does that work for the median (as opposed to the mean)? Asking because median rejects outliers better than the mean.
- d_tr 5y agoIt works the same way. Nine times the clocks, three times smaller standard deviation for both the mean and the median of their readings. In a normal (and any symmetric) distribution these two are the same anyway, so their difference will tend to zero as you increase the number of clocks and the measurements from a single reading of all the clocks look more and more like a bell curve. This is asymptotic behavior so the "rejects the outliers better" aspect does not come into play, and I do not know whether it is useful in this situation or not.
- jmalicki 5y agoIn large samples the error bars for the median are sqrt(pi/2) times the error bars for the mean if the underlying distribution is normal (the link gives more general results, but that helps give some intuitions about being directly comparable) https://en.wikipedia.org/wiki/Median#Sampling_distribution https://en.wikipedia.org/wiki/Median#Sampling_distribution