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

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 = (\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

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 = (\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