Statistics Notation

[ampakine]

In my lecture notes on confidence intervals the lecturer wrote this:

Recall that measurements tend to follow a normal distribution. To describe the normal distribution and answer useful questions (as in the previous chapter), we need to know two numbers; the expectation or mean μ and the standard deviation (square root of the variance) σ. Then the quantity we measure X follows the normal distribution:

X ~ N(μ, σ²)

 

I don't understand the notation of that bolded text. I know X is a random variable, μ is the population mean and σ is the population standard deviation but what does the ~ mean? Also the N(μ, σ²) I assume means normal distribution but is that some kind of standard notation for distributions? For example if I said N(23,9) would that mean the normal distribution with a mean of 23 and standard deviation of 9?

[CraigD]

... what does the ~ mean?

~ (tilde) usually means “about”, “approximately”, “roughly”, etc. It’s sometimes combined with an equal sign to make something like [math]\approx[/math] or [math]\simeq[/math]. Another common “about” notation is a dot over another symbol, like [math]\dot=[/math].

 

Also the N(μ, σ²) I assume means normal distribution but is that some kind of standard notation for distributions? For example if I said N(23,9) would that mean the normal distribution with a mean of 23 and standard deviation of 9?

Any notation is only as standard as understood by the majority of its readers, but I think you have this right. Note the exponent attached to the standard deviation variable σ (sigma), though: you should have said “N(23,9) is a normal distribution with a mean of 23 and a variance of 9”, or “standard deviation of 3”.