When should one of mean, mode, and median be used over the other
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If I’m trying to figure out my average cost for buying a set of products, mean is how I do it. That’s probably the best example for that. When you’re looking at REALLY big sets of numbers and individual outliers are not a problem, mean works great, again with things like investments or large purchases.
If its something where the individual experience matters, median works great. What are the average winnings of a lottery player? If I ask for mean, the number might be 3 dollars for a 5 dollar ticket. If you look at median it’s 0, since significantly more than half of tickets win nothing. One pertinent at my job- the mean amount of experience nurses at my job have in the specialty is something like 4 years. The median that they have is 8 months, because there’s a handful of people with 10 to 20 plus propping up the average, so the average patient gets a nurse with less than a year of experience.
Mode works similar to median where you’re trying to grasp the average individual experience- it’s rare that it’s a better tool. It works great for sets with really high variability to try to establish a pattern or find bottlenecks in a process. Looking at personal annualized incomes, for example, there’s a near infinite number of values for them, with the median in the 10s of thousands and a mean closer to 100s, but the mode is 0. Also a fun one for personally reported heights by men- the median might be 5 foot 9, the mean around there too, but 6 foot might be the mode, since there’s a LOT of rounding up as you approach that height and get close to that number.
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