Question

A report includes a statement that the​ "average" test score of applicants to medical schools is 28.4. What is the role of the term​ "average" in​ statistics? Should another term be used in place of​ average?

Answer 1

Answer:

See explanation below.

Step-by-step explanation:

The average is measure of central tendency that is also called sample mean and is calculated from the following formula:

$\bar X = \frac{\sum_{i=1}^n X_i}{n}$

This is an estimator of the population mean and is unbiased since the expected value for the estimator is the same parameter as we can see here:

$E(\bar X)=\frac{\sum_{i=1}^n E(X_i)}{n} =\frac{n\mu}{n}=\mu$

And is important because is the most common measure of central tendency reported on any study.

Is important to remember that this measure can be affected by outliers , for this case when we have outliers is better use the median as a measure of central tendency