Calculates the mode(s) of a list of numbers.

L₁ - To store the user-inputted list of numbers

L₃ - The mode(s) of the original list of numbers

Ans - The mode(s) of the original list of numbers (alternates)

L₂ - Intermediate calculation storage

X - Weregoose's version only

TI-83/84/+/SE/CSE/CE

```
:ClrList L₂,L₃
:iL₁(1)+sum(L₁=L₁(1→L₂(1
:For(L,2,dim(L₁
:If not(max(L₁(L)=imag(L₂
:iL₁(L)+sum(L₁=L₁(L→L₂(1+dim(L₂
:End
:For(L,1,dim(L₂
:If real(L₂(L))=max(real(L₂
:imag(L₂(L→L₃(1+dim(L₃
:End
```

The mode of a list is the value that occurs most often within the list. This routine will find the mode and, if there are any ties, will display all modes. Examples:

```
:{1,2,3,3,4
Mode = {3}
:{5,5,6,6,7
Mode = {5,6}
```

# Alternate Routines

```
:SortA(L₁
:Repeat min(0≠ΔList(L₂
:{0→L₂
:ΔList(L₁→L₃
:For(θ,1,dim(L₃
:If not(L₃(θ
:L₁(θ→L₂(1+dim(L₂
:End
:L₂→L₁
:End
:ΔList(cumSum(L₂
```

This version coded by Trenly is slightly shorter than the above routine by kg583 and produces the same output, which is saved in Ans rather than L₃. However, the original list in L₁ is modified in the process, so make sure to backup that list somewhere else if you need it later.

```
:1+max(abs(L₁→X
:L₁+Ans
:While max(Ans
:Ans→L₁
:SortD(L₁
:L₁augment({0},not(ΔList(L₁
:End
:sum(L₁ xor 0→dim(L₁
:L₁-X
```

This version written by Weregoose is very similar to Trenly's in form and function. The output is, again, in Ans and lists all modes, but does also modify L₁ in the process. Note the advanced use of the xor function.

```
seq(sum(0>L₁-X),X,1,max(L₁)+1)+1
ΔList(Ans
1+sum(not(cumSum(Ans=max(Ans
```

This version, also written by Trenly is more compact and notably does not use either SortA( or SortD(. However, this version is limited to positive non-zero integers. Another limitation of this snippet is that multi-modal lists only return the lowest value mode.

```
seq(sum(0>L₁-X),X,1,max(L₁)+1)+1
ΔList(Ans
1=(Ans-(max(Ans)-1
seq(XAns(X),X,1,dim(Ans→L₂
While not(A>dim(L₂
1+sum(not(cumSum(L₂=0→A
seq(L₂(A+(A≥Ans)),A,1,dim(L₂)-1→L₂
End
L₂
```

You will notice some similarities to the previous routine in this routine. This routine was also written by Trenly, and is based on the previous routine. However, this version supports multi-modal arrays even though it is still limited to the set of natural numbers.

.