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I have a graph with an asymmetrical distribution (spectral response for some sensor). The graph is plotted as efficiency values versus vavelength. I must determine the median wavelength. Help please, my statistics is so rusty !
I have determined the mean value of the efficiency - the values on the y-axis, and considered selecting the wavelength (x-value) corresponding to that value - but that doesn't seem to give me a relevant answer, and it is not even close to the center of the plot (even in the case where it should be). I thought of cheating and just getting the median of the graph - but the graphs are weird. In one case, the graph has a fairly rectangular shape (rise, sort of plateau but with mountains and valleys, then fall), in another case, there is a skewed peak on the left and another tiny bump on the right.
I would appreciate any suggestions ! Thank you !

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    Do you want the median or the mean? How did you determine the mean of the efficency? Do you have a sample?2012-05-01
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    Used Excel's mean, and noticed that it was wrong.2012-05-02

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I was eventually able to find the mean as $\dfrac{\sum (p_i x_i)} { \sum (p_ i)} $ .

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    I am not even sure -- What $\pi$ and $x_i$ are? Why don't you tell us what you wanted to find? What you are given? It is not even clear, even from the question.2012-05-04
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    Seriously ? You replace pi (probability index i to go along with xi) with π, then tell me it makes no sense and mark it down ?2012-05-05
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    See wikipedia - mean of a probability distribution - expected value: http://en.wikipedia.org/wiki/Expected_value2012-05-05
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    I have now edited it accordingly. But, if you wanted $p_i$ then, you would atleast write `p_i` and not pi. Looking around the site will tell you this site allows TeX mark up. Go through my edit by clicking on the timestamp available above my name. I have now removed my downvote. (FWIW, I do know what the expected value of a random variable is, but _still_ feel that you should write your answer more clearly.) Regards,2012-05-05
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    Sorry I didn't know how to format math expressions - I have only formatted code so far - and I don't have rights to edit other people's posts to see their formatting (too few points). Thank you.2012-05-05
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    You can always edit posts, but since you have fewer points, they would be peer reviewed. Nonetheless, you can always click on `Edit` to see the source of the post. (<-- this does not need rep.) Regards,2012-05-05