Generate numbers in R

Question

In R, how can I generate N numbers that have a mean of X and a median of Y (at least close to).

Or perhaps more generally, is there an algorithm for this?

Answer 1

There is an infinite number of solutions.

Approximate algorithm:

1. Generate n/2 numbers below the median
2. Generate n/2 numbers above the median
3. Add you desired median and check
4. Add one number with enough weight to satisfy your mean -- which you can solve

Example assuming you want a median of zero and a mean of twenty:

R> set.seed(42)
R> lo <- rnorm(10, -10); hi <- rnorm(10, 10)
R> median(c(lo,0,hi))
[1] 0                         # this meets our first criterion
R> 22*20 - sum(c(lo,0,hi))    # (n+1)*desiredMean - currentSum
[1] 436.162                   # so if we insert this, we the right answer
R> mean(c(lo,0,hi,22*20 - sum(c(lo,0,hi))))
[1] 20                        # so we meet criterion two
R> 

because desiredMean times (n+1) has to be equal to sum(currentSet) + x so we solve for x getting the expression above.