       Counting number of numbers in a large list between two valus

• To: mathgroup at smc.vnet.net
• Subject: [mg114499] Counting number of numbers in a large list between two valus
• From: Lyle <lgordon at gmail.com>
• Date: Sun, 5 Dec 2010 21:57:05 -0500 (EST)

```Dear Listers,

I have a large (5-20million) one dimensional list of real numbers and
I want to count the number of entries in the list that lie between 2
specific values (x1, x2). I need to run the function for a number of
different ranges.

ie. number of list entries (l), where x1 <= l <= x2

I've tried:

tallydata[{x1_, x2_}] := Count[data, x_ /; x1 <= x <= x2]

and

tallydata[{x1_, x2_}] := Length[Select[data, x1 <= # <= x2 &]]

which takes a little bit longer.

The best I've managed is (this last one might be off by 1 or 2 but
this doesn't really matter to me):

sorteddata = Sort[data];
nf = Nearest[sorteddata];
tallyrange[{x1_, x2_}] :=
First[Position[sorteddata, First[nf[x2]]]] -
First[Position[sorteddata, First[nf[x1]]]]

which takes between 1 and 2 seconds but I was hoping there might be a
faster way to do this?

Any help would be great!

Thanks,
Lyle Gordon

Northwestern University

```

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