Using one table for multiple arguments

Question

So I want to plot two graphs (on the same plot). One which is the $\frac{\sum_{i=0}^n x_i}{n}$ and the other $\frac{\sum_{i=0}^n x_i}{n-1}$ where x is a set created by RandomInteger[{a,b},n] and then have n slowly increase. I was wondering if this would be a sort of nice convergence plot over a large interval. The problem is as seen I want all of them to use the one {n,c,d} table for their iteration but Sum wants a copy, Plot wants a copy and RandomInteger wants the length of it. How can I use one of it for all of those?

Answer 1

Assuming you want each of the summations over two different randomly generated lists:

{Total@ RandomInteger[{a, b}, #]/#, 
     Total@ RandomInteger[{a, b}, #]/(# - 1)} & /@ Range[2, n] // 
  Transpose // ListLinePlot

Answer 2

Adding an additional (optional) parameter for increment, define

 datalistPlot[a_Integer, b_Integer, c_Integer, d_Integer, e_Integer: 1] := 
 Module[{left = Mean@RandomInteger[{a, b}, c]},{
 Transpose@
 Table[{left=(n - 1) left/n + RandomInteger[{a, b}]/n, n left/(n - 1)}, {n, c, d, e}], 
 {c, d}, 
 (a + b)/2
 }] 
 // ListLinePlot[#[[1]], 
 GridLines -> {None, {{#[[3]], Directive[Red, Thick]}}}, 
 DataRange -> #[[2]], PlotRange -> {Automatic, #[[3]] + {-1, 1}}] &

and use as

datalistPlot[list[0, 10, 10, 500, 10]

to get