Determining the population mean

Question

So I asked 10 random people in the gym some questions and this is how it went:

1. Do you know how to swim? If the person responded no then I was not allowed to ask them any more questions. However, if the person responded yes then I had to ask them their age. In addition, I took note of their gender.

Basically, I have a table that looks something like this:

Now, my professor wants us to do this question: Estimate the average age of males and females who can swim in San Francisco.

So what I did was took the sum (which was $150$) of the age and divided by $10$ and got the average age to be $15$.

Now this is where I am confused: My professor asked "Include your best guess as to what the population mean will be" but how would I be able to get the population mean from this data if this is a sample?

Also, the professor gave a part for correlation and said "Describe direction, form, and strength of the relationship." However, don't you need two different variables to create a relationship? In this case, the only variable is age.

Answer 1

"Include your best guess as to what the population mean will be"

It turns out that the sample average $\bar X$ is an unbiased estimator of the population average $\mu$: $$E[\bar X] = \mu.$$ Thus, the sample average is your best guess.

However, don't you need two different variables to create a relationship?

Yes, you do. You're being asked to make some inference regarding age and gender. In which case, you have all the information needed: age and gender.

Answer 2

You have two variables: age and sex. For sex you can use an indicator: $0$ for male and $1$ for female or vice-versa.

You cannot know the population mean, but you were asked to estimate it based on the sample.

Whether your sample is representative of those who were at the gym might bear examination.