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## Statistical questions

Current time:0:00Total duration:7:51

# Statistical and non statistical questions

## Video transcript

- [Instructor] 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. And we could call the ones
where we need statistics as statistical questions,
statistical questions. And 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 a pass at it, and now 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 they're not all gonna be the same age. There's gonna 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? Would 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 wanna find some
type of central tendency, an average, a median age for this. So this is absolutely
a statistical question. And 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. And so we'll 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 maybe on average
how fast do cats run? And then we could compare those averages, or we could 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, very heavy dogs. And so what you would want to do here, because we have variability
in each of these, is you might want to come
with some central tendency. On average, what is
the median wolf weight? What's the average, the mean wolf weight? Compare that to the mean dogs' weight. So once again, since we're
speaking in general about wolves not a particular wolf,
and in general about dogs, 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, a particular dog to a particular wolf. We could 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 at the 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'd also probably want to know does it rain 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, and 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, the mode 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 aren't known. They can be measured. Both the rainfall in
Singapore can be measured, the rainfall in Seattle can be measured. And assuming that this has already happened and we can measure 'em, then we can just find the difference. So you don't need statistics here. You just have to have
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. You know, exactly how
you're driving the car, are you turning, are you
going in a straight line. And same thing for 70 miles an hour. So when we're saying 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 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, all English professors don't get paid the same amount, and all math professors don't
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. I guess especially if we assume that this is in a particular year. Let's say, and let's
just make it that way. 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, 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.