# Algoritma keur ngitung varian

Rumus pikeun ngitung populasi varian:

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

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

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

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 = ${\displaystyle {\sqrt {\mathit {Variance}}}}$= 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