Statistical and non statistical questions | Probability and Statistics | Khan Academy

What I want to do in this video is think about the types of questions that we need statistics to address and the types of questions that we don't need statistics to address. We could call the ones where we need statistics as statistical questions. I'll circle the statistical questions in yellow, and I encourage you to pause this video and try to figure this out yourself first.

Look at each of these questions and think about whether you think you need statistics to answer this question or you don't need statistics. Whether these are statistical questions or not. So I'm assuming you've given up a stat it not unless we can go through this together.

So this first question is: How old are you? So we're talking about how old is a particular person. There is an answer here, and we don't need any tools of statistics to answer this, so this is not a statistical question. How old are the people who have watched this video in 2013? Now, this is interesting. We're assuming that multiple people will have watched this video in 2013, and if they're not all going to be the same age, there's going to be some variability in their age.

So one person might be 10 years old, another person might be 20, another person might be 15. So what answer do you give here? Did you give all of the ages? But we want to get a sense of, in general, how old are the people? So this is where statistics might be valuable. We might want to find some type of central tendency, an average, a median age for this. So this is absolutely a statistical question.

You might already be seeing kind of a pattern here. The first question we were asking about a particular person, there was only one answer. Here, there's no variability in the answer. The second one, we're asking about a trait of a bunch of people, and there's variability in that trait; they're not all the same age. So we only need statistics to come up with some features of the data set to be able to make some conclusions. We might say, on average, the people who have watched this video in 2013 are 18 years old or 22 years old, or the median is 24 years old, whatever it might be.

Do dogs run faster than cats? So once again, there are many dogs and many cats, and they all run at different speeds. Some dogs run faster than some cats, and some cats run faster than some dogs. So we would need some statistics to get a sense of, in general, or on average, how fast do dogs run? And then it may be, on average, how fast do cats run? Then we could compare those averages or we can compare the medians in some way. So this is definitely a statistical question.

Once again, we're talking about, in general, a whole population of dogs, the whole species of dogs versus cats, and there's variation in how fast dogs run and how fast cats run. If we were talking about a particular dog and a particular cat, well then there would just be an answer. Does dog A run faster than cat B? Well, sure, that's not going to be a statistical question; you don't have to use the tools of statistics.

And this next question actually fits that pattern. Do wolves weigh—actually, no, this fits the pattern of the previous one. Do wolves weigh more than dogs? So once again, there are some very light dogs and some very heavy wolves. So those wolves definitely weigh more than those dogs, but there are some very, very heavy dogs.

So what you would want to do here—because we have variability in each of these—is you might want to come up with some central tendency: on average, what's the median wolf weight? What's the average, the mean wolf weight? Compare that to the mean dog weight. So once again, since we're speaking in general about wolves, not a particular wolf, and in general about dogs and we're trying to—and there's variation in the data and we're trying to glean some numbers from that to compare—this is definitely a statistical question.

Definitely a statistical question. Does your dog weigh more than that wolf? And we're assuming that we're pointing at a particular wolf. So now this is the particular; we're comparing a dog to a particular dog to a particular wolf. We can put each of them on a weighing machine and come up with an absolute answer. There's no variability in this dog's weight at least at the moment that we weigh it, no variability in this wolf's weight at the moment that we weigh it. So this is not a statistical question.

So I'll put an X next to the ones that are not statistical questions. Does it rain more in Seattle than Singapore? So once again, there's variation here, and we would also probably want to notice if it rains more in Seattle than Singapore in a given year over a decade or whatever. But regardless of those questions, however we ask it, in some years it might rain more in Seattle, in other years it might rain more in Singapore. Or if we just pick Seattle, it rains a different amount from year to year; in Singapore, it rains a different amount from year to year.

So how do we compare? Well, that's where the statistics could be valuable. There's variability in the data, so we can look at the data set for Seattle and come up with some type of an average, some type of a central tendency and compare that to the average, the mean, the mode—whatever you want—probably wouldn't be that useful here—to Singapore. So this is definitely, definitely a statistical question.

Definitely statistical. What was the difference in rainfall between Singapore and Seattle in 2013? Well, these two numbers are known; they can be measured. Both the rainfall in Singapore can be measured, the rainfall in Seattle will can be measured, and assuming that this has already happened and we can measure them, then we can just find the difference. So you don't need statistics here; you can just find both of these measurements and subtract the difference.

So not a statistical question. In general, will I use less gas driving at 55 miles an hour than 70 miles per hour? So this feels statistical because it probably depends on the circumstance. It might depend on the car, or even for a given car, when you drive at 55 miles per hour, there's some variation in your gas mileage. It might be how recent an oil change happened, what the wind conditions are like, what the road conditions are like, the weather, I mean, there’s how exactly you’re driving the car—are you turning? Are you going in a straight line? And the same thing for 70 miles an hour.

So when we're seeing in general, there's variation in what the gas mileage is at 55 miles an hour and at 70 miles an hour. So what you’d probably want to do is say, well, what's my average mileage when I drive at 55 miles an hour and compare that to the average mileage when I drive at 70? So because we have this variability in each of those cases, this is definitely a statistical question.

Do English professors get paid less than math professors? So once again, not all English professors get paid the same amount, and not all math professors get paid the same amount. Some English professors might do quite well; some might make very little. Same thing for math professors. So we’d probably want to find some type of an average to represent the central tendency for each of these. So once again, this is a statistical question.

This is a statistical question. Does the most highly paid English professor at Harvard get paid more than the most highly paid math professor at MIT? Well, now we're talking about two particular individuals. You could go look at their tax forms, see how much each of them get paid, and I guess especially if we assume that this is in a particular year—let's say in 2013, just so that we can remove some variability that they might make from year to year—make it a little bit more concrete.

So if this was: Does the most highly paid English professor at Harvard get paid more than the most highly paid math professor at MIT in 2013? Then you have an absolute number for each of these people, and then you could just compare them directly. And so when we're talking about a particular year, particular people, then this is no longer a statistical question, or it isn't a statistical question.