Finding the Mode(s) from a list

[Henry]

I've been trying to figure out the best and fastest way to find the mode(s) of a list. By using a frequency routine and then just a loop to find repeats of the frequency, the mode is found:

ClrList L₂,L₃,L₄
SortA(L₁
For(A,1,dim(L₁
L₁(A→L₂(1+dim(L₂
sum(L₁=Ans→L₃(dim(L₂
A-1+Ans→A
End
For(A,1,dim(L₃
If max(L₃)=L₃(A)
L₂(A→L₄(1+dim(L₄
End
ClrList L₂,L₃

List four is the output of the modes

Any suggestions? There is also some theorem for finding the mode stating that mean - mode is approx. equal to 3(mean - median), http://mathworld.wolfram.com/Mode.html

Also, there is a quick routine posted on the TI-basic vault: http://weregoose.unitedti.org/#ModeCalculator

:imag(max(Ansi+E9seq(sum(Ans=Ans(A)),A,1,dim(Ans
But it only finds one mode if there exists more than one.

[Galandros]

That seems the normal and best way to find all the modes with sure.

To initialize the lists without giving errors (if they don't exist) use:
0->dim(L₂
instead of
ClrList L₂

Then in the end to clear the lists, delete them with:
DelVar L₂
DelVar L₃
because DelVar for some odd reason does not need a new line you can type in TI-BASIC:
DelVar L₂DelVar L₃

[Weregoose]

This was my distraction while losing a game of Settlers of Catan...

seq(sum(L1=L1(X)),X,1,dim(L1
Ans=max(Ans
For(X,1,dim(Ans
If Ans(1)min(Ans≠L1(X
augment(Ans,{L1(X
ΔList(cumSum(Ans
End

The output is in Ans. (This runs into strange issues when the modes are zero or one.)