How can I compute the mean, standard deviation, minimum, and maximum of a vector without using MATLAB's std function?

I need to write a function that computes the mean, standard deviation, minimum & maximum values and range of a ten element vector, without using the std function. Instead i've been given the equation (last x is meant to be x-bar but couldn't work out how to write it):

 σ =√((1/N)(∑_(i=1)^n)▒(xᵢ-x) )

N is the number of data points (10 in this case) and x-bar is the mean value of x.

I can use any other functions except std.

[Randy Souza]

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Answer 1

[Cedric]

Say you have

 >> x = [4, 8, 7, 5] ;
 >> b = 6 ;

If you wanted to subtract b to each element of x, you would do it with:

 >> y = x - b
 y =
    -2     2     1    -1

this is a vector operation: in one shot, you operate on all elements, without having to use a loop. Now if you look up for element-wise operations in MATLAB, you will realize that for operators which have a matrix definition, like the product *, there is an element-wise version whose syntax involves a dot, e.g. .*. Same for ^ and .^.

You might not know what a matrix product is, but the element-wise product is the usual product applied to each element. Now I let you experiment with that, e.g. if you wanted to square all elements of a vector.

[will]

i understood most of what you said but i'm still unsure with what i need to do for the question? sorry to be a pain

[Cedric]

You are not a pain, but, for obvious reasons, I cannot give you the answer. The last hint that I can give you is the following: usually in MATLAB we don't perform sums by looping over a range, summing/stacking terms, in the way the mathematical expression (with ∑) is suggesting. Instead, we compute a vector of all the terms of the sum, e.g.

 >> x = [7, 5, 6] ;                   % Defined by previous computation.

note that these are numerical values, that we then sum:

 >> theSum = sum(x)
 theSum = 
           18

Now you have all the information that you need.. just proceed by small steps: try to compute terms that have to be summed, sum them, perform other operations if needed.