In the description / help of matlab for the function var it says that the sum is normalized by default with N-1 instead of N that is why you get different results:
x = [1,1,1,2];
mean_x=mean(x);
var1=sum((x-mean_x).^2)/length(x)
var2=sum((x-mean_x).^2)/(length(x)-1)
var1 =
0.1875
var2 =
0.2500
You can find here a discussion about the difference of using N-1 rather than N. Var allows you to choose between both normalization by setting the second parameter to 0 default N-1 or 1 for N
statistics - MATLAB var function returns weird results - Stack Overflow
Variance function in matlab
what is var function in matlab?how does it works in image processing?
Question About MATLAB Variance Built-in Function!
In the description / help of matlab for the function var it says that the sum is normalized by default with N-1 instead of N that is why you get different results:
x = [1,1,1,2];
mean_x=mean(x);
var1=sum((x-mean_x).^2)/length(x)
var2=sum((x-mean_x).^2)/(length(x)-1)
var1 =
0.1875
var2 =
0.2500
You can find here a discussion about the difference of using N-1 rather than N. Var allows you to choose between both normalization by setting the second parameter to 0 default N-1 or 1 for N
Just to add on to the point above
V = var(A,w) specifies a weighting scheme. When w = 0 (default), V is normalized by the number of observations-1. When w = 1, it is normalized by the number of observations. w can also be a weight vector containing nonnegative elements. In this case, the length of w must equal the length of the dimension over which var is operating.
Thus, doing var(x,1) will give you the correct answer
Matlab reference
Hey everyone,
I hope, everyone is doing well. I would like to ask question about matlab's var built-in function.
I just generated uniformly distributed random signal using rand.
%% noisy signal generation
noise=rand(len,1)';
%% variance formula for uniformly distributed signal
%% var(signal)=((l-k)(l-k+2))/12;
param=noise(end)-noise(1);
variance=((param*(param+2)))/12;
%% this is how matlab calculate the var function
RESID = noise - mean(noise);
VAR = sum(RESID.*conj(RESID)) / len;When I tried to execute the variance calculation manually, I got the different result compared to built-in function. Basically results are for variance=0.0023 and VAR=0.0847.
I know that rand function generates numbers randomly between 0 and 1. But this difference is normal? Matlab built-in function normalizes the result. Can we assume that formula for the variance calculation already somehow normalized? ( I am not sure this is accurate to say!)
Try this:
var = sum(a.^2)/(length(a)-1) - (length(a))*mean(a)^2/(length(a)-1)
var =
335.2111
var is computed as (unbiased) sample, not population variance.
For a complete explanation you can read here.
From the matlab documentation,
VAR normalizes Y by N-1, where N is the sample size. This is an unbiased estimator of the variance of the population from which X is drawn, as long as X consists of independent, identically distributed samples.
but
Y = VAR(X,1) normalizes by N and produces the second moment of the sample about its mean. VAR(X,0) is the same as VAR(X).
so that
>> var(a,1)
ans =
301.6900
An unbiased sample variance is given by:
>> 1/(length(a)-1) * sum((a-mean(a)).^2)
ans =
335.2111
