How to calculate mean and variance?

Greetings. I have generated a vector of 10,000 complex samples. I want to calculate the Mean and Variance of the samples. How can I do it without using the built-in functions _ mean()_ and * var()* ? and how do I do that in a loop? Please help.

Thank you

[Ana Soph]

How can convert to 1 minute to 10 minutes, a wind directio data ? please, i have a matrix fo 1440x31

Answer 1

[Jorge Mario Guerra González]

Since you want to do it without using the functions, just do:

    A=rand(1000,1); %your array
sum1=0;
for i=1:length(A)
  sum1=sum1+A(i);
end
M=sum1/length(A); %the mean
sum2=0;
for i=1:length(A)
    sum2=sum2+ (A(i)-M)^2;
end
V=sum2/length(A); %Varaince

[Stephen23]

@Jorge Guerra : you should never use the variable name sum, because this will shadow the inbuilt sum function (so it will not work). For the same reason never use variable names cell, length, size, i, j, table, etc. Beginners make the mistake of re-assigning name of important functions, and are then surprised when the inbuilt function does not work.

Note that you can use which to check if a name if already defined.

[Walter Roberson]

We do not encourage giving complete answers to homework questions.

[SHRIVATHSA S.]

Thank you @Jorge Guerra for the answer. It was really helpful

[Jorge Mario Guerra González]

@Stephen Cobeldick absolutely agree, that was just a fast script I wrote to show the proccedure. I edited the answer

Answer 2

[Walter Roberson]

Mean is the average -- the sum divided by the number of entries.

Variance is the sum of the squares of (the values minus the mean), then take the square root and divided by the number of samples

You can vectorize the calculation using sum().

To use a for loop to calculate sums, initialize a running total to 0, and then each iteration of the loop, add the current value to the running total.

[SHRIVATHSA S.]

Thank you @Walter Roberson for the answer. That helped me a lot

[Jurgen]

This answer contradicts the variance formula on the MATLAB website (no square root). Oh and wikipedia disagrees. The MATLAB variance assumes a uniform probability distribution. A very important assumption.

[John D'Errico]

@ Jurgen - you make no sense in some of what you said, although you are correct about the square root being incorrect in this answer. Variance has no square root in it.

A variance is something you can compute from the data, or for a population, but there is no assumption about the underlying distribution, nor is there any need to make such an assumption.

Answer 3

[Olayemi Akinsanya]

P=[10:2:70]

i wrote a script for variance, it gives me a value of 320. when i check with var(P), it gives me a value of 330.6667. can someone advice what i did wrong.

[Walter Roberson]

You probably divided by N (number of items) instead of dividing by (N-1) (number of degrees of freedom). See https://stats.stackexchange.com/questions/100041/how-exactly-did-statisticians-agree-to-using-n-1-as-the-unbiased-estimator-for

Answer 4

[Nikos Lambadakis]

A=rand(1000,1); %your array

sum((A(1:end)-sum(A(1:end))./length(A)).^2)/(length(A)-1) % the same result as

% var(A)

var(A) == sum((A(1:end)-sum(A(1:end))./length(A)).^2)/(length(A)-1)

ans =

logical

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