# Median doesn't behave like mean on a vector of vectors

**URL:** <https://discourse.julialang.org/t/median-doesnt-behave-like-mean-on-a-vector-of-vectors/107156>\
**Category:** General Usage\
**Created:** [December 5, 2023, 10:39am UTC](https://discourse.julialang.org/t/median-doesnt-behave-like-mean-on-a-vector-of-vectors/107156 "2023-12-05T10:39:36Z")\
**Posts on this page:** 4\
**Page:** 1

<div class="post-metadata">

**Author:** ![ovt](https://avatars.discourse-cdn.com/v4/letter/o/87869e/32.png) [@ovt](https://discourse.julialang.org/u/ovt)\
**Post date:** [December 5, 2023, 10:39am UTC](https://discourse.julialang.org/t/median-doesnt-behave-like-mean-on-a-vector-of-vectors/107156/1 "2023-12-05T10:39:36Z")

</div>

```julia
julia> using Statistics

julia> y = [[i for i in 4*(j-1)+1:4*j] for j in 1:3]
3-element Vector{Vector{Int64}}:
 [1, 2, 3, 4]
 [5, 6, 7, 8]
 [9, 10, 11, 12]

julia> mean(y)
4-element Vector{Float64}:
 5.0
 6.0
 7.0
 8.0

julia> median(y)
6.5

```

---

<div class="post-metadata">

**Author:** ![rocco\_sprmnt21](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/rocco_sprmnt21/32/20127_2.png) [@rocco\_sprmnt21](https://discourse.julialang.org/u/rocco_sprmnt21)\
**Post date:** [December 5, 2023, 11:22am UTC](https://discourse.julialang.org/t/median-doesnt-behave-like-mean-on-a-vector-of-vectors/107156/2 "2023-12-05T11:22:04Z")

</div>

```julia
# mid = div(first(inds)+last(inds),2) == 2

julia> partialsort!(y,2 )
4-element Vector{Int64}:
 5
 6
 7
 8

julia> middle(partialsort!(y,mid))
6.5

```

It appears that the median code calculates the middle of the median vector, if **there is** a median vector.  
if it isn’t there, it goes into error

```julia

julia> yy = [[i for i in 4*(j-1)+1:4*j] for j in 1:4]     
4-element Vector{Vector{Int64}}:
 [1, 2, 3, 4]
 [5, 6, 7, 8]
 [9, 10, 11, 12]
 [13, 14, 15, 16]

julia> median(yy)
ERROR: MethodError: no method matching middle(::Vector{Int64}, ::Vector{Int64})

```

---

<div class="post-metadata">

**Author:** ![ovt](https://avatars.discourse-cdn.com/v4/letter/o/87869e/32.png) [@ovt](https://discourse.julialang.org/u/ovt)\
**Post date:** [December 5, 2023, 8:51pm UTC](https://discourse.julialang.org/t/median-doesnt-behave-like-mean-on-a-vector-of-vectors/107156/3 "2023-12-05T20:51:27Z")

</div>

Indeed. I don’t think that this is an expected behavior.

```julia
julia> y = [[i for i in 4*(j-1)+1:4*j] for j in 1:3]
3-element Vector{Vector{Int64}}:
 [1, 2, 3, 4]
 [5, 6, 7, 8]
 [9, 10, 11, 12]
julia> y[2][4]=99
99

julia> median(y)
52.0

```

I guess the main issue (if it is one, I don’t know if this behavior is intentional) is coming from `>` “working” on vectors:

```julia
julia> a = [1,99,99];b=[2,1,1];

julia> a>b
false

```

it just compares the first index of `a` and `b`, or the next one in case of equality. I understand why this behavior makes sense for testing `a==b` when they are a collection, but the meaning of `a>b` when they are collection hardly makes sense for me.

---

<div class="post-metadata">

**Author:** ![rocco\_sprmnt21](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/rocco_sprmnt21/32/20127_2.png) [@rocco\_sprmnt21](https://discourse.julialang.org/u/rocco_sprmnt21)\
**Post date:** [December 6, 2023, 10:20am UTC](https://discourse.julialang.org/t/median-doesnt-behave-like-mean-on-a-vector-of-vectors/107156/4 "2023-12-06T10:20:43Z")

</div>

> [@ovt](#):
>
> I guess the main issue (if it is one, I don’t know if this behavior is intentional) is coming from `>` “working” on vectors:

mmmhh … it seems to me that the behavior of ‘\>’ on a pair of vectors is the “normal” one for lexicographic comparison.  
Rather, I draw attention to the median!() method which, for a vector with an odd number of elements, calculates the middle of the median element.

```julia
function median!(v::AbstractVector)
    isempty(v) && throw(ArgumentError("median of an empty array is undefined, $(repr(v))"))
    eltype(v)>:Missing && any(ismissing, v) && return missing
    any(x -> x isa Number && isnan(x), v) && return convert(eltype(v), NaN)
    inds = axes(v, 1)
    n = length(inds)
    mid = div(first(inds)+last(inds),2)
    if isodd(n)
        return middle(partialsort!(v,mid))
    else
        m = partialsort!(v, mid:mid+1)
        return middle(m[1], m[2])
    end
end

```

If the elements are themselves vectors then middle behaves as per the contract

```julia
middle(a::AbstractArray)
Compute the middle of an array a, which consists of finding its extrema and then computing their mean.

```

in your example: `(5+99)/2=52.0`