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# Frequency

Calculates how often values occur within a given set of ranges.
Controller: CodeCogs  C++

## Frequency

 template std::vectorfrequency( int n T* data int m T* bin )
This function calculates how many values in the given set of data fall within each interval of the bin array, while also calculating the number of values below and above the bin extremas. For example, use this function to count the number of test scores that fall within ranges of scores.

## Example:

```#include<iostream>
#include<codecogs/statistics/moments/frequency.h>
int main()
{
double
x={160, 130, 100, 70, 52, 28, 27,26, 14.25, -1, -7 },
y={10, 25, 40.7, 61.3};
std::vector<int> result=Stats::Moments::frequency(11,x,4,y);
std::cout<<"The corresponding frequencies for the x array are:";
std::cout<<std::endl;
for(int i=0; i<result.size(); i++)
std::cout<<result[i]<<" ";
std::cout<<std::endl;
return 0;
}```
Output:
```The corresponding frequencies for the x array are:
2 1 3 1 4```
i.e. 6 numbers in total fall outside the designated range

### Parameters

 n the total number of data points in array data data an array of n data point m the total elements in array bin, which should be 1 more than the number of bins you need to define bin the bounds of each bin, therefore given the lower and upper boundaries and shared common boundaries to each bin, there should be (number bins +1) values.

### Returns

the number of times the values in the data set occur within each defined bin. Values falling below the range given in bin are returned in element, while values falling above the given range are returned in element[m+1]. Therefore the return array is always two larger that the bin array, contains m+2 elements.

### Authors

Will Bateman (Sep 2007)
##### Source Code

Source code is available when you buy a Commercial licence.

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## Class Frequency

This class is usefull in generating a histogram of a sequence of dispersed numbers. The class is initialised with the expect range of numbers (min and max) and the number of bins to create. The class will actually create 2 further bins, that captures values that fall below min and another than catches values that fall above max.

### Example 1

```#include <codecogs/statistics/distributions/continuous/beta/randomsample.h>
#include <codecogs/statistics/moments/frequency.h>

int main(int argc, char* argv[])
{
Stats::Dists::Continuous::Beta::RandomSample m_Betagen;
Stats::Moments::Frequency bins(20,0,1);

for(int i=0; i<10000; i++)
{
double val = m_Betagen.genReal(0.2, 3);
}

for(int i=0;i<22;i++)
printf("\n%d %lf %d %lf ",i, bins.get_x(i), bins.get_count(i), bins.get_freq(i));
}```
Output
```0 -0.025000 0 0.000000
1 0.025000 7095 0.709500
2 0.075000 944 0.094400
3 0.125000 569 0.056900
4 0.175000 355 0.035500
5 0.225000 269 0.026900
6 0.275000 196 0.019600
7 0.325000 143 0.014300
8 0.375000 133 0.013300
9 0.425000 70 0.007000
10 0.475000 63 0.006300
11 0.525000 53 0.005300
12 0.575000 32 0.003200
13 0.625000 36 0.003600
14 0.675000 19 0.001900
15 0.725000 7 0.000700
16 0.775000 7 0.000700
17 0.825000 5 0.000500
18 0.875000 2 0.000200
19 0.925000 2 0.000200
20 0.975000 0 0.000000
21 1.025000 0 0.000000```
##### Source Code

Source code is available when you buy a Commercial licence.

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## Members of Frequency

#### Frequency

 Frequency( int N double min` = 0` double max` = 1` )[constructor]
Establishes the Frequency contains which will hold the underlying histogram of results
 N the number of bins to create min the start of the smallest bin max the end of the largest bin

#### Get X

 doubleget_x( int i )
Returns the coordinate of middle of each bin: where is the width of each bin equal to max value minus the min value divided by the number of bins.
 i the i th value

#### Get Freq

 doubleget_freq( int i )
 i the i th value