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## Statistical questions

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

# Statistical and non statistical questions

## Video transcript

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. And I'll circle the statistical
questions in yellow. 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. I'm assuming you've
given us a pass at it. Now we can go through
this together. 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
that they're not all going to be the same age. There's going to be some
variability in their age. One person might
be 10 years old. Another person might be 20. Another person might be 15. So what answer do you give here? Do 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. 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? 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. 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. Actually, no, this fits the
pattern of the previous one. Do wolves weigh more than dogs? Once again, there are some very
light dogs and some very heavy wolves. So those wolves definitely
weigh more than those dogs. But there's some very,
very, very heavy dogs. And so what you 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's the
median wolf weight? What's the average,
the mean wolf weight? Compare that to the
mean dog's 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. Does your dog weigh
more than that wolf? And we're assuming that we're
pointing at a particular wolf. Now this is the particular. We're comparing 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. This is not a
statistical question. I'll put an x next
to the ones that are not statistical questions. Does it rain more in
Seattle than Singapore? Once again, there
is variation here. And we would 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. In other years, it might
rain more in Singapore. Or if we just picked 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-- the mode probably wouldn't be that useful
here-- to Singapore. So this is definitely
a statistical question. 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
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 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? 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, 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. 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. 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? Once again, all
English professor 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. Once again, 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, especially if we assume that
this is in a particular year. 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. 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. So when we're talking
about a particular year, particular people, then it
isn't a statistical question.