Question

A defunct website listed the​ "average" annual income for Florida as​ $35,031. What is the role of the term average in​ statistics? Should another term be used in place of​ average?

Answer 1

Answer:

For this case the average is an statistic unbiased for the population parameter $\mu$

And the average is calculated with the following formula:

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

Where n represent the sample size

N represent the population size, and X the observations for this case the annual income.

This statistic is an unbiased estimator of the population mean since $E(\bar X) = \mu$

After calculate the average they got:

$\bar X= 35031$

And we can use the term "sample mean" instead of the average, and is a measure of central tendency for the data

Step-by-step explanation:

For this case the average is an statistic unbiased for the population parameter $\mu$

And the average is calculated with the following formula:

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

Where n represent the sample size

N represent the population size, and X the observations for this case the annual income.

This statistic is an unbiased estimator of the population mean since $E(\bar X) = \mu$

After calculate the average they got:

$\bar X= 35031$

And we can use the term "sample mean" instead of the average, and is a measure of central tendency for the data