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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). This is because, without the benefit of an intercept, the regression could do worse than the sample mean in terms of tracking the dependent variable (i.e., the numerator could be greater than the denominator).

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. Estimate meanlog 6.0515 sdlog 0.3703 how to calculate the mean and sd of this distribution? 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 have represented standard deviation as ±sd before in publications But i like to have opinions on this Is it appropriate to use the notation '±' with sd One takes the pairwise difference of each point of data [ the mean of the differences ] and the other takes mean a and subtracts it from mean b [ the difference of the means ]

While the differences can be calculated to come out the same, the confidence intervals for each are different I am confused as to which formula to use for which situation. After calculating the sum of absolute deviations or the square root of the sum of squared deviations, you average them to get the mean deviation and the standard deviation respectively The mean deviation is rarely used.

If $\theta=4$ how to you find the mean and variance

My guess was to plug in $4$ of course and then integrate that function from $0$ to infinity As for the variance i honestly have no clue I have not taken statistics in a while so i admit i am a bit rusty

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