Suppose I have the following formula. It calculates the average value of $n$ evenly spaces numbers on the range from $L$ to $H$.

1/n Sum[x, {x, L, H, (H - L)/(n - 1)}]

My question is, how can I use Mathematica to compute the average value of the above, when I remove a specific number from the sequence. I am looking for an elegant solution, perhaps one that removes a particular index, or some other method I have not thought about.

Ideally, the solution should allow me to plot the average of the numbers on the Y-axis, and the removed index on the X-axis.


3 Answers 3


Probably easiest to just manage this as a list:

list[l_, h_, n_] := Table[x, {x, l, h, (h-l)/(n-1)}];
ListPlot[Table[Mean[Drop[list[1, 10, 10], {i}]], {i, 1, 10}]

Example Plot of Average vs. Dropped Index

If you really want to do this with sums, it'd be possible to modify the formula slightly by subtracting off the missing term:

1/(n - 1) (Sum[x, {x, l, h, (h - l)/(n - 1)}] - ((h - l)/(n - 1) i + l))

(-l - (i (h - l))/(-1 + n) + (Floor[n] (-h - l + 2 l n + h Floor[n] - l Floor[n]))/(2 (-1 + n)))/(-1 + n)

Plotting this for h->10, l->1, and n->10, over {i, 0, 9, 1} provides the same plot as previously shown.


The maths is very simple. For any list ls

ls = Range[1, 19];
m = Mean[ls]
(* 10 *)

we can "downdate" our estimate of the mean

x = 15;
Mean[Complement[ls, {x}]] == Module[{n = Length[ls]}, (n m - x)/(n - 1)]
(* True *)
f[n_, l_, h_] := Module[{r = Subdivide[l, h, n - 1]},   
   MapIndexed[{#, Mean[Drop[r, #2]]} &, r]]

ListPlot[Callout[#, {##}]& /@ f[6, 11, 21]]

enter image description here


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.