Smooth/histogram a 2D set

Question

I have a 2D dataset like this one: {{x1,y1}, {x2,y2},...} I need to smooth/histogram the data in such a way that binning is over the x-coordinate, while counting/height is over the y-coordinate. Let me explain.

Given the following input, bin-width=0.2 and height-function=Mean[].

data = {{0.1,1.0}, {0.2,2.0}, {0.3,3.0}, {0.35,3.5}, {0.4,4.0}, {0.5,5.0}};

The output would be:

{(1 + 2)/2, (3 + 3.5 + 4)/3, 5/1}

The average of y-values from the first two data points goes into the first bin, the following three points form the second bin etc...

Answer 1

Let's start with your sample data:

In[1]:= data = {{0.1, 1.0}, {0.2, 2.0}, {0.3, 3.0}, {0.35, 3.5}, {0.4, 4.0}, {0.5, 5.0}};

First we can use GatherBy to group entries by bin:

In[2]:= GatherBy[data, Ceiling[First[#], 0.2] &]

Out[2]= {{{0.1, 1.}, {0.2, 2.}}, {{0.3, 3.}, {0.35, 3.5}, {0.4, 4.}}, {{0.5, 5.}}}

Then select the second element of each pair (Last) and calculate the means:

In[3]:= Mean[Last /@ #] & /@ %

Out[3]= {1.5, 3.5, 5.}

Answer 2

I propose:

data = {{0.1, 1.0}, {0.2, 2.0}, {0.3, 3.0}, {0.35, 3.5}, {0.4, 4.0}, {0.5, 5.0}};

Mean /@ Reap[#2 ~Sow~ Ceiling[#, 0.2] & @@@ data][[2]]

{1.5, 3.5, 5.}

Answer 3

Another offering making use of BinLists:

data = {{0.1, 1.0}, {0.2, 2.0}, {0.3, 3.0}, {0.35, 3.5}, {0.4, 
    4.0}, {0.5, 5.0}};

Smoothed[data_, binSize_] := 
 With[{xs = data\[Transpose] // First, ys = data\[Transpose] // Last},
   Mean@ys[[#]] & /@ (Flatten[Map[Position[xs, #] &, #]] & /@ 
     BinLists[xs, 0.2 + $MachineEpsilon])]

Smoothed[data, 0.2]

(* ->  {1.5, 3.5, 5.}  *)