Arithmetical mean above max

Question

Claire 2013-8-16

1
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/84876-arithmetical-mean-above-max

Is it possible that, due to precision matter, arithmetical mean of an array is above max of same array ?

Is Matlab then limiting mean to min-max interval (at least for display) ?

Regards Claire

1 个评论
显示 -1更早的评论隐藏 -1更早的评论

Image Analyst 2013-8-18

I doubt it - have you actually observed this? If so, what is the code?

请先登录，再进行评论。

请先登录，再回答此问题。

Answer 1

David Sanchez 2013-8-16

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/84876-arithmetical-mean-above-max#answer_94416

The mean value ( either geometric or arithmetic ) of an array can never be above the maximum value of the array. Matlab does not have to limit the result of the operation.

0 个评论
显示 -2更早的评论隐藏 -2更早的评论

请先登录，再进行评论。

Answer 2

Claire 2013-8-16

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/84876-arithmetical-mean-above-max#answer_94417

Is there no case where precision can produce some error as

mean = 1.000000012

max = 1.00

1 个评论
显示 -1更早的评论隐藏 -1更早的评论

David Sanchez 2013-8-16

I don't know of any case. However, if dealing with very small numbers, the result will be prone to some error. In any case, achieving an average of a set above the maximum value of that set, (beside being against its definition) is extremely unlikely even when working with very small numbers.

请先登录，再进行评论。

Answer 3

Jan 2013-8-17

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/84876-arithmetical-mean-above-max#answer_94499

编辑：Jan 2013-8-17

在 MATLAB Online 中打开

Matlab's mean(x) uses the calculation sum(x) / numel(x). Therefore it suffers from the numerical instabilities of sum:

x = [1e17, 1, -1e17]
sum(x)

This replies 0 instead of 1, because the limited floating point precision does not allow to distinguish 1e17 and 1e17+1. This means, that in sum() small values can vanish, when they are surrounded by large numbers with different sign, and of course this matters partial sums also. But this cannot lead to the situation, that the sum is larger than numel(x)*max(x), except if you reach the overflow such that sum() replies Inf. Then sum(x)/n differs from sum(x/n).

v = [realmax, realmax]
mean(v)

(What does this reply? I cannot check this currently.)

So perhaps this would be a better implementation of MEAN:

function m = meanX(x)
m = sum(x) / numel(x);
if ~isfinite(m)
  m = sum(x / numel(x));
end

A furter effect appears for large arrays, when Matlab distributes the partial sums to different threads. Then the floating point effects depend on the number of cores also, but here the sum cannot exceed numel(x)*max(x) also, except for the above mentioned exception.

See FEX: XSum for a summation with higher accuracy.