weighted average w/ matlab

Hi guys, I have calculated different errors over a range.

let's say a range with a linear space from 100 to 150.

For this range I calculate a variable Y so Y(range).

Now I want to calculate the mean of the variable, but I want to give the values close to 125 more weight than the values close to 100 and 150, with the heaviest weight being 125.

I can't seem to figure it out, can someone help me out?

Answer 1

[Udit Gupta]

You can do something like -

 weight=normpdf(range,centerPoint,spread);
 wAvg = sum(Y(range).*weight)/sum(weight);

In you example centerPoint will be 125, and larger the spread more slowly the weight will decrease away from centerPoint.

[Regi streer]

the spread function does not work (Undefined function or variable 'spread'.)

[Udit Gupta]

spread is not a function. It can be any value. Bigger the value bigger the spread is. For example spread = 100 will provide a wide and gentle slope and spread = 50 will produce a steeper slope.

[Regi streer]

ah okay, it's a normal distribution i missed that. Thanks!

Answer 2

[dpb]

Have to decide how much you want the weights to be, but the general idea would be sotoo--

 >> y=randi([100 150],40,1);  % some random data
>> mean(y)                    % mean should be near 125
ans =
  123.9750
>> w=(y/100).^2;w=w/mean(w);  % compute a weight dependent on y; normalize to 1 overall...
>> [min(w) max(w)]            % what's look like???
ans =
    0.6400     1.4399
>> mean(y.*w)                 % how much did we change it???
ans =
  128.0471
>>

[Regi streer]

But this does not give me exactly more weight at 125 in my problem right?

[dpb]

My bad; somehow I read too quickly that the max weight was to be 150, not midpoint. Use a functional with a max at 125; could be the normal pdf as another poster showed or whatever you wish but the same idea works.