I was reading here
the sum of the deviations about the mean will be 0, except for possible rounding.
Could anyone explain me the what does it mean? I know about sum of deviations from mean being zero but what about this except for possible rounding?
Best Answer
When a mean is computed, it's not computed to infinite precision. As a result, the computed sum of deviations around a mean can be a little different from zero.
We can see this, for example, in R, like so:
x <- rnorm(1000) # generates 1000 standard normal random numbers, puts them in x d <- x - mean(x) # compute the deviations from the mean and put them in d sum(d) # add the deviations [1] 2.026851e-14 Now $2 times 10^{-14}$ is very small… but it isn't exactly zero.
If you want to investigate in detail how finite precision computation is different from algebra, this is a handy resource.
If you compute a mean by hand and round your values off to say 3 decimal places, you'll see the same thing – frequently the sum of deviations about the mean is slightly different from zero.
Similar Posts:
- Solved – Find true negatives in a confusion matrix
- Solved – Area under Precision-Recall Curve (AUC of PR-curve) and Average Precision (AP)
- Solved – Logistic regression gradient descent converge
- Solved – Are truncated numbers from a random number generator still ‘random’
- Solved – MAE and Precision for Collaborative Filtering Recommender Systems