So we have arithmetic mean (AM), geometric mean (GM) and harmonic mean (HM). Their mathematical formulation is also well known along with their associated stereotypical examples (e.g., Harmonic mea...
The mean is the number that minimizes the sum of squared deviations. Absolute mean deviation achieves point (1), and absolute median deviation achieves both points (1) and (3).
When studying two independent samples means, we are told we are looking at the "difference of two means". This means we take the mean from population 1 ($\\bar y_1$) and subtract from it the mean from
Context is everything here. Are these theoretical variances (moments of distributions), or sample variances? If they are sample variances, what is the relation between the samples? Do they come from the same population? If yes, do you have available the size of each sample? If the samples do not come from the same population, how do you justify averaging over the variances?
What does it imply for standard deviation being more than twice the mean? Our data is timing data from event durations and so strictly positive. (Sometimes very small negatives show up due to clock
The mean you described (the arithmetic mean) is what people typically mean when they say mean and, yes, that is the same as average. The only ambiguity that can occur is when someone is using a different type of mean, such as the geometric mean or the harmonic mean, but I think it is implicit from your question that you were talking about the arithmetic mean.
I'm struggling to understand the difference between the standard error and the standard deviation. How are they different and why do you need to measure the standard ...
I also guess that some people prefer using mean squared deviation as a name for variance because it is more descriptive -- you instantly know from the name what someone is talking about, while for understanding what variance is you need to know at least elementary statistics. Check the following threads to learn more:
The above calculations also demonstrate that there is no general order between the mean of the means and the overall mean. In other words, the hypotheses "mean of means is always greater/lesser than or equal to overall mean" are also invalid.
