Question

State whether each of the following statements is true or false. If false, then explain what would make the statement true (a) The central limit theorem explains why the mean is always at the center of a distribution.

(b) The standard error of the mean is the standard deviation of a sampling distribution of sample means.
(c) The mean of a sampling distribution is equal to the population mean from which samples are selected.

Answer 1

Answer: (a) False; (b) False; (c) True;

Explanation: The alternative (a) is false because, in a distribution, its center is not the mean but the median. Although both mean and median means average value, mean is a value calculated as if all the distribution would have the same value; Median is the actual middle centered value of a distribution, that's why it is the Median the value in the center of a distribution;

The alternative (b) is false due to the definition of standard error of the mean: Standard Error of Mean (SEM) is the measurement of how far the mean sample is from the population sample.