       Re: grouping and averaging {x,y} pairs of data

• To: mathgroup at smc.vnet.net
• Subject: [mg37229] Re: grouping and averaging {x,y} pairs of data
• From: BobHanlon at aol.com
• Date: Thu, 17 Oct 2002 00:09:17 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```In a message dated 10/16/2002 4:30:28 PM, deb at alceon.com writes:

>I have a list of 17,000+ {x,y} pairs of data
>
>   each x value is a positive integer from 1 to 100+
>
>   each y value is a positive real number
>
>As a *short* example, let's consider:
>
> data = {{3,1},{4,3},{3,2},{1,10},{4,2},{1,6},{5,2},{2,5},{7,1}}
>
>I want to group the data by the x value and report the arithmetic average
>of the y values in each group.
>
>For the example, i want to report:
>
> output = {{1,8},{2,5},{3,1.5},{4,2.5},{5,2},{6,0},{7,1}}
>
>In this example, x=6 does not occur so i report the average y = 0.
>
>Can anyone suggest a way to do this efficiently?/
>

The basic approach is

(Plus @@ #)/Length[#] & /@
Split[Sort[data], #1[] == #2[] &]

{{1, 8}, {2, 5}, {3, 3/2}, {4, 5/2}, {5, 2}, {7, 1}}

To fill in the gaps:

dataAvg[data_] :=
Module[{val = First /@ data, xData},
xData = Join[data, {#, 0} & /@
Complement[Range[Max[val]], val]];
(Plus @@ #)/Length[#] & /@
Split[Sort[xData], #1[] == #2[] &]];

dataAvg[data]

{{1, 8}, {2, 5}, {3, 3/2}, {4, 5/2}, {5, 2}, {6, 0}, {7, 1}}

Bob Hanlon

```

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