If a quantity cannot be negative (such as a mass), then standard deviation isn't the best choice.
EDIT: Yes, because the Gaussian distribution extends to +/- infinity; davrosthedalek explains it best, below.
EDIT: Yes, because the Gaussian distribution extends to +/- infinity; davrosthedalek explains it best, below.
It's more interesting if you calculate the distribution of the sum of rolling 100 dices. It's easy to calculate, becuase μ=100*3.5=35, σ=sqrt(100*105/36)~=17.07... But now the distribution is very similar to a Gaussian with μ=100*3.5=35 and σ=sqrt(100*105/36)~=17.07... https://en.wikipedia.org/wiki/Central_limit_theorem They are not equal because the sum of the roll of 100 dices is bounded between 100 and 600 and the Gaussian is not bounded. For most applications, you can just use the Gaussian instead of the exact distribution.
Alternate reply: Gaussian approximation to the binomial is perfectly valid in all sorts of cases.
However, the 7 here is basically (x - mu)/sigma, so it is normalised (in that sense), anyway.
A good example is efficiency measurements. I can't count how often I have seen students say something like: Our detector is 99%+-3% efficient. Obviously a detector can't be 102% efficient.
I have a master's degree in statistics and this is the first I'm hearing about it.
> Our detector is 99%+-3% efficient. Obviously a detector can't be 102% efficient.
In the absence of any other context I'd guess that they're using an approximation to a confidence interval that might be perfectly fine if the estimated value was nearer the center of the allowable range.
Hearing 99+-3% is a very strong indication that the person used an incorrect way to determine the uncertainty, most likely by taking the square-root of counts. But you are right, if the efficiency would be around 50%, that approximation is not so bad.
(One should not confuse a CI with a range of plausible values, in other words.)