No Stupid Questions

Mode is easily be screwed up by data distribution, it's used for almost nothing.

1, 2, 3, 4, 5, 45, 98, 100, 100

Mode = 100 Mean = 39.8 Median = 45

Mean is used because it handles most data-sets well, it just gets screwed up a lot when there are big outliers. That's when we use Median instead.

For example we use Median a lot for household incomes, there's a lot of data points, but there are some ridiculously wealthy people and some people that make absolutely nothing. Mode doesn't really work in this situation, because it would likely just be 0.

Because they mean very different things. Imagine you tallied the spending of 5 people in your restaurant:

10 15 30 100 150

First of all that distribution has no mode, so let's then check the next 2 customers.

10 15 20 30 100 150 150

Cool, now checked with 7 people this, and we can say the following.

The mode is to spend 150. Almost no one does this, but that is the mode regardless.

The median is 30, this tells you that half the people spend more than this, and half the people spend less than it. However it doesn't give you an accurate idea, because the people who spend less spend close to it, but the people who spend more spend way more. So if a guy spends 35 he would look like a high spender, but in fact he probably should be in the low spending category.

The average is 67.85, no one spent this amount, but this tells you that if a person spends more than that he's a high spender, so of someone came in and spent 35 you would know he's not one of your high spending customers.

Now let's see how each of those numbers is at predicting how much 7 customers would spend, let's look at the same values, where the customers spent 475. The mode tells you that people will spend 1050, that's absolutely wrong. The median tells you that they'll spend 210, that's also very wrong. The average however tells you that they'll spend 475 which is the exact number.

This is the same for every other statistics, even if it doesn't make any sense to say that people have an average of 2.3 kids, if you were planning on receiving 10 random families they would probably have 23 kids in total. Average is good at predicting large groups, and that's the information we usually care about when we're trying to express a large group in a single number. If you want a second number the obvious choice is the standard deviation, in the example above the standard deviation is 63.76 this gives you an idea on how accurate is your average at predicting, so in the case above not very accurate at all, but if we imagine that the number of kids above had a standard deviation of 0.2 you can be 68% certain that the 10 families will have between 21-25 kids, or 95% certain that they will have between 19-27 kids, or 99.7% certain that they will have between 17-29 kids. Working with the level of confidence in a prediction allows you to evaluate certainty at doing things. If you only knew that the median was 2 kids or that the mode was 1 kid you couldn't predict things with any accuracy.

If you generate 1000 random numbers from 0 to 100 with a uniform distribution, the mean is going to be roughly 50, whereas the mode couid be anything. Which one is more representative?

It all depends on how it is distributed, discretely or continuously, and mode tends to fail the most often which is why it's rarely used.

If you asked a random group of people what their annual salary was, you may get many answers of "zero" or something round like "100k/six figs,", which would become the mode which doesn't accurately represent a middle value.

If you ask a group of working people (to remove zero) to give their last year's post-tax salary to the nearest cent as close as possible, then there is a good possibility there is no mode, as everyone has a different exact salary, due to taking different benefits, hours, tax obligations and so on.

It's not that we don't use mode, there are definitely times mode is used. It's just that mean (and median as well) contain a lot more useful information about distributions that we often care about. For a normal distribution mean, median, and mode should all be identical. So why do we use mean? Because mathematically, the mean is what underpins the formula for the normal distribution, not median or mode, and when you're talking about doing math with normal distributions mean is the thing to talk about (along with standard deviation).

We use median a lot too, you probably just don't hear it called median very often. The median is useful in non-normal distributions, and it defines the 50th percentile, so along with the 25%-ile and 75%-ile you've got your quartile distributions. We use these all the time to talk about grades in schools, or when we talk about home prices distributions in a given area, or salaries within a given field.

We use mode too, again just by a different name most of the time. Any time you've asked "what's the most common blank" you're basically asking for a mode. When we talk about "average" income in a country, we're usually actually talking about median or mode. Favorite animal? Answered as a mode.

You have to use the right statistical tool for your question: unfortunately English doesn't do a good job of conveying this without math jargon.

When you have a qualitative measure on an axis mode can get really weird. Let's say we have a dance class with 3 13 year olds, 4 14 yos, 5 15 yos, 4 16 yos, 5 17 yos, 3 18 yos, and a group of six retirees that signed up as a lark for someone's birthday and are all 72 years old.

That dance class is mostly composed of teenagers but the mode is 72 year olds. I think mode is a terrible measure but it's very close to what we'd like to phrase as "mostly" the issue is that it's very strict about bucket boundaries while we humans like to group things arbitrarily.

In addition to the other answers here, the mode doesn't work with continuous variables.

Because we can't have nice things.

If you downvote this post, you are a humorless pedant

I came here to say that I highly enjoyed your title, OP.

titlegold +10