 
Note
 There are any number of ways of obtaining almost any statistic you can name.
 Which method is best will depend upon your circumstances.
 Most basic statistics formulae assume you are using a calculator, and working from the original data.
 In practice, such formulae are a waste of time, given the ready availability of statistical computer programms.
 So the formulae below attempt to provide some insight as to each statistic's reasoning and assumptions.
 For simplicity, these formulae make no assumptions as to how the data were obtained.
y_{(i=random)}
provides an estimate of the average
 where
 y is a list of values
 assuming the values may be numeric or nonnumeric
 y_{(i)} is the ith value of y
 assuming y contains n values, and i is a whole number from one to n
 random is a randomly selected integer (from i=1 to n) where every value of i is equally likely to be selected, and the outcome of that selection cannot be predicted in advance
sum(y/n)
gives the mean of y
 where
 sum(y/n) is the sum of y/n, or the (sum of y)/n, or the sum of y_{(i)}/n
 assuming y is a list containing n numbers
 y_{(i)} is the ith value of y
 assuming i is a whole number from one to n, and y is summed for all values of y
y_{[mean(r)]}
gives the median
 where
 y is a list of n rankable values
 assuming, when y is nonnumeric, that ranking does require criteria external to y.
 y_{[r]} is the rth ranked value of y
 assuming there are n ranks, in the range 1 to n
 mean(r) is the arithmetic mean of the n ranks
f/n
gives the proportion
 where
 y is a list of n values
 assuming y may be numeric or non numeric, and either equal A, or do not equal A
 y_{(i)} is the ith value of y
 assuming y contains n values, and i is a whole number from one to n
 f is f_{(y(i)=A)} the sum of the number of items whose value equals A
the value of A may be any desired value for comparison
 note
when y can only equal 1 or 0, then f_{(y(i)=A)} is the sum of y, so the proportion is simply the mean of y.

pn
gives the rank of the pth quantile
 where r is the rank
 y_{r} is the rth ranking value of a list (y) containing n, different, rankable items
 assuming n is extremely large (approaching infinite)
 p is the proportion of ranks below r,
 when r is a fraction you interpolate, or choose the best value.

squareroot(variance)
gives the 'population' standard deviation
 where the variance is the mean squarederror, sum(e^{2})/n, sometimes described as the 'population variance'
 assuming each value of e is the difference between the value of y, and the mean of y
 y contains n numbers

