Finding frequency of range of numbers in Mathematica

Question

Given a list of numbers in Mathematica, how would I extract from that list the total number of numbers between numbers a and b that I specify?

Answer 1

The most direct way is simply:

Count[data, x_ /; a <= x <= b]

There are however much faster ways for most data, this one thanks to Carl Woll:

Tr@Unitize@Clip[data, {a, b}, {0, 0}]

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Carl Woll's method is particularly fast, but as yoda pointed out, it fails if your list contains zeros, and your range also straddles zero. Here is another method from Kevin J. McCann that handles this case, and is still very fast:

Tr@UnitStep[(data - a)*(b - data)]

As a pure function [data, a, b]:

Tr@UnitStep[(#-#2)*(#3-#)]&

Answer 2

Here is one approach that you can try:

freq[a_, b_, list_] := Total@Boole@Cases[list, x_ :> a <= x <= b]
lst = RandomInteger[10, 20]
Out = {6, 1, 1, 6, 3, 1, 10, 0, 2, 10, 3, 5, 9, 1, 5, 5, 3, 8, 2, 3}

freq[3, 6, lst]
Out = 9

An alternate approach using IntervalMemberQ is

freq[a_, b_, list_] :=
 Total@Boole@IntervalMemberQ[Interval[{a, b}], list]

Answer 3

another approach is

NumberOfNumbers[lst_?ListQ, lwr_?NumberQ, upr_?NumberQ] := 
 Length@Select[lst, (lwr <= # <= upr) &]

D

Answer 4

Please look into BinCount:

In[176]:= BinCounts[Range[30], {{2, 11/2}}]

Out[176]= {4}

Compare with direct count:

In[177]:= Count[Range[30], x_ /; 2 <= x < 11/2]

Out[177]= 4