When should one of mean, mode, and median be used over the other
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These are all ways of determining what the “average” of something is.
The mean just finds the answer in the middle and leaves it at that. Useful when you want to know the average of something reasonably continuous where you need to know roughly what to expect based on the data you have. Things like how long does it take to travel a particular route to work or how much rainfall you expect to have each month are usually looked at as the Mean. The catch is that it can be influenced by a limited number of outliers (really big or really small values)
Median is where the “average” answer is one that is reasonably common but it’s still better for continuous data. It’s more useful where you have extreme values at one end of the scale that can make the mean look higher than is actually common. Pay data is a good example where this is used. No-one earns less than zero money in their job and a few people earn massive amounts. If you take the mean, it can make it look like the average worker has a lot more money than most people actually do. The median pay is the the amount that half the population earns more than and half earn less than which is usually a lot more useful.
The mode is the most common answer. This is mostly only useful when the answers are discrete – that is, you can either be one or the other not in between. With continuous data, 1.99, 2 and 2.01 are all different answers unless you group them first. On the other hand, calculating whether the average pet is a cat or a dog is impossible with a mean – if 1/3 of pet owners have a cat, 1/3 have a dog and 1/3 have both then the mean is half cat, half dog which doesn’t make any sense. Also good for things like what colour car do people prefer or anything else where you have distinct answers and can’t end up in between
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