Algoritma keur ngitung varian

Rumus pikeun ngitung populasi varian:

{\mathit {Variance}}={\frac {n\sum _{i=1}^{n}x_{i}^{2}-(\sum _{i=1}^{n}x_{i})^{2}}{n^{2}}}

Rumus pikeun ngitung unbiased estimasi populasi varian tina sampel "terhingga" nyaéta:

{\mathit {Variance}}={\frac {n\sum _{i=1}^{n}x_{i}^{2}-(\sum _{i=1}^{n}x_{i})^{2}}{n(n-1)}}

Cara ngitung bakal leuwih gampang kaharti dina tabel di handap ieu di mana nilai méan = 8.

  
    i 
    xi 
    xi-méan 
    (xi-méan)2
  

    (index) 
    (datum) 
    (deviation) 
    (squared deviation)
  

    1 
    5 
    -3 
    9
  

    2 
    7 
    -1 
    1
  

    3 
    8 
    0 
    0
  

    4 
    10 
    2 
    4
  

    5 
    10 
    2 
    4
  

    n=5 
    sum=40 
    0 
    18
  

méan = 40/5 = 8
variance = (5*338 - 40²)/(5 * 4) = 4.5
standard deviation = ${\sqrt {\mathit {Variance}}}$ = 2.12

Catetan: Ngitung varian sacara lengkep:

338 = [5² + 7² + 8² + 10² + 10²]
40 = [5 + 7 + 8 + 10 + 10]

Algoritma

Algoritma sederhana keur ngitung varian saperti di handap ieu:

double sum;
double sum_sqr;
double variance;
long n = data.length; // the number of elements in the data array (the actual syntax is language-specific)

for i = 0 to n
 sum += data[i];
 sum_sqr += ( data[i] * data[i] );
end for

variance = ((n * sum_sqr) - (sum * sum))/(n*(n-1));

Algoritma

Algoritma séjén keur jumlah angka anu loba

double avg;
double var;
long n = data.length; // number of elements

for i = 0 to n
 avg = (avg*i + data[i]) / (i + 1);
 if (i > 0) var += (var * (i - 1) + (x - avg)*(x - avg)) / i;
end for

return var; // resulting variance

i	x_i	x_i-méan	(x_i-méan)²
(index)	(datum)	(deviation)	(squared deviation)
1	5	-3	9
2	7	-1	1
3	8	0	0
4	10	2	4
5	10	2	4
n=5	sum=40	0	18