the explanation is clear and totally right,the average of partial standard deviation can not be seen as the global std.
Is there any standard way of computing mean and std? Mathematically it should be calculated using the pixel-wise approach which is computationally very expensive for large datasets. I am currently working on an image dataset with 2,60,000 images in train dataset. For batchwise calculations, where Average of minibatch variances is used for the variance calculation, it is still not accurate. Which still raises the question about the accurate implementation or atleast a standard approach for calculating these values. If anybody could help in highlighting the standard widely used approach to calculate these values then please comment on this post.