Why does the variance not coincide with the autocorrelation function in 0?

Hello everyone, I am a civil engineering student and I am practising some signal processing topics. I was wondering, why in my script the correlation function calculated in 0 does not agree with the variance of my signal? They are very close (within a factor of 1000).

Thanks to all of you who answer, your work is valuable.

clear all; close all; clc;
t = 0:1000;
x = randn(1,length(t));
subplot(2,1,1);
plot(t,x)
ylabel('Amplitude')
xlabel('Time sample')
title('Gaussian noise signal')
[y,lags]=xcorr(x);
subplot(2,1,2);
plot(lags,y);
ylabel('Correlation output')
xlabel('Delay')
title('Autocorrelation of AWGN')

y(lags==0)

ans = 1.0556e+03

var(x)

ans = 1.0529

Answer 1

[Sharmin Kibria]

var(x) = sum((x-mean(x)).^2)/1000 while y(lags==0) is just calculating sum(x.^2). Because of the normalization var does your result is off by a factor of 1000.