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Is the sum of an absolute value is the same of their absolute values?
The sum of the absolute values of two numbers is greater or equal than the absolute values of the sum. It will be equal if both are positive or both are negative; greater if one is positive and one is negative. Try it out with some sample numbers!
What does weighted average mean?
The weighted arithmetic mean is used, if one wants to combine average values from samples of the same population with different sample sizes: : The weights wi represent the bounds of the partial sample. In other applications they represent a measure for the reliability of the influence upon the mean by respective values. rhinostar
What is independent values?
sample data drawn from one population is completely unrelated to the selection of sample data from the other population.
If three samples have means of 10 20 and 15 what is their grand mean?
The grand mean can only be calculated if the three samples are of equal size. In this case, the grand mean is the mean of the three sample means. In this case, it would be (10+20+15)/3 = 15. However, in the sample sizes are not equal you must take the weighted mean. One option would be to assign, to each of the three means, an importance that reflects its sample size. So, if in the above example, the sample sizes were a, b and c the grand mean would be (10a + 20b + 15c)/(a+b+c) It is easy to show that the grand mean becomes the mean of the three sample means when a = b = c.
What is sample?
A sample is a subcollection of members selected from a population. (Ref Triola, Elementary Statistics). A sample may be real or hypothetical. Real- Ten patients at the hospital were interviewed about the care they received. Hypothetical- Repeatedly drawing n independent, and identical values X1, X2... Xn from a normal distribution to form a random sample, the mean of this sample should conform to a normal distribution, if the sample size is greater than 30.
