I'm a private math tutor. I'm fairly new at this, and this semester is the first time I've been tutoring for a statistics class at a community college. I enjoy experimenting and learning about ways to explain math.
I'd like to get some feedback on explaining sampling and distributions to students who struggle, especially those who don't have a lot of cognitive power.
In any math topic, to help them understand math concepts I relate those to everyday experiences. Here is my idea for sampling and distributions.
I say imagine that you are a hairdresser (or substitute other profession they can relate to). I say, imagine it's the end of your work day and you're reflecting back on what happened. You think about the number of clients you had (an example of a discrete random variable), the amount of time spent cutting (a continuous random variable), or anything you like.
I say, imagine explaining your workday to a friend. I get them to imagine this hypothetical day and the language they would use. For instance, would they say to their friend, it was an unusual day with a lot of clients? Or a typical day with an average number, or typical number of minutes spent cutting? What are some ways in which days can be unusual?
Hopefully they start to form this mental picture of both the experiences of a single day (a sample) and how days vary over time, including what patterns are more frequent (a distribution).
We talk about some of the factors that might affect the distribution of clients. Are holidays very busy, while Fridays slow? We think about the population of all potential clients in this city and parameters of this population, and how they would affect what the hairdresser sees.
I haven't done this yet, but even the Central Limit Theorem could be explained by asking them to differentiate between day to day variation, and the variation of weekly averages.
So, just wondering if the statisticians here have similar or better ideas.