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Statistical questions | Data and statistics | 6th grade | Khan Academy - YouTube
Channel: Khan Academy
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- [Voiceover] As we start
exploring the world of statistics,
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it's worth asking ourself,
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what is the word statistics even mean?
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Statistics is really a
broad category of things
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that you might do with data.
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So it generally deals with
data, collecting data.
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So actually let me write these down.
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It's involving collecting data,
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collecting data.
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You could present data
in tables or charts,
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or just as lists of numbers,
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or however you might do it.
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It is analyzing the data,
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analyzing, analyzing,
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presenting and analyzing data.
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So this whole class of just all this stuff
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that you might do with
data to answer a question
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or try to figure out what's going on,
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or just to learn about the world,
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the whole class of things
is called statistics.
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Now an idea that will
come up very frequently
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in statistics is the
notion of variability.
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Variability.
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In everyday language, variability,
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it's how much something is ...
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How much does it vary?
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How much does it change?
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It's the same notion in statistics.
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In statistics, variability
is the degree to which
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data points are different from each other,
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the degree to which they vary.
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Just as an example of that
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to just make it a little
bit more concrete,
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let's say you were to go to five people,
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and you were to ask them,
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how many bricks did you eat yesterday?
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Each of the people say, well I ...
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Person one says, "I
don't eat bricks at all.
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"I don't even know how to do that.
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"I ate zero bricks."
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Then next person says zero,
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the next person says zero,
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fourth person says zero,
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and the fifth person says zero.
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Fair enough, so that was our data point
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on the different data points on ...
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And I'm already doing statistics
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just by going out there and asking them
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how many bricks they ate.
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Then I ask them how many grapes
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did you eat yesterday?
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The first person says "I ate zero grapes."
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But the next person says
"I survive on grapes.
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"I ate 235 grapes."
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The next person says, "Yeah I like grapes.
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"I ate 17 grapes."
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Then the person after that
says that they five grapes.
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Then next person also survives on grapes,
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even to a larger degree.
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They ate 318 grapes.
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So if you look at these two data sets,
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one is the number of bricks
someone ate yesterday,
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the other one is how many
grapes they ate yesterday,
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you immediately see that
there's more variability here.
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All of these data points are zero,
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while these, they change a good bit
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from data point to data point.
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So we have a sense that
there is more variability
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in this data set.
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Now one of the things we will start doing
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a lot in statistics is try to measure
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how much more, how much variability is.
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How can we can quantify that?
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How can we put a number on it?
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How can we measure variability?
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This is a big aspect of statistics,
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but we won't do that in this video.
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There are future videos for doing that.
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But just as we go into
the world of statistics,
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we should think about
when should our brain
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even start getting into statistics mode,
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thinking about the tools
that we have at our disposal,
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about collecting data and
measuring variability,
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and measuring and finding numbers
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that somehow represent a pool
of data that has variability.
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So the question we should ask ourselves is
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what questions in the world
are statistical questions?
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So statistical,
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statistical questions.
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So let's come up with a
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definition for statistical questions,
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the type of question
where we would want to
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start bringing out our
statistical toolkit.
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One possible way to think about
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when you need to bring out
your statistical toolkit
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is these are questions
that to answer them,
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to answer,
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you need to collect data with variability.
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To answer, you need
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to collect
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data with variability.
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I apologize for my handwriting.
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Data with variability.
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That's W-I-T-H.
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Data with
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variability.
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So you're saying, okay
that kinda makes sense,
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but I need to see some tangible questions
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or tangible examples of things
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that are statistical questions
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and things that are not
statistical questions.
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I would say fair enough.
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Let's look at some examples.
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So here I have six questions,
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and I encourage you to
pause this video right now.
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Before I work through it, think about it.
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Based on this definition
of a statistical question,
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which of these questions are statistical,
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would require your statistical toolkit,
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and which of these are not statistical?
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So assuming you had a go at it,
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let's go through these one by one.
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So the first question,
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how much does my pet grapefruit weigh?
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You know, it's bizarre to begin with
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to have a pet grapefruit,
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but is this a statistical question?
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What do I need to do to answer it?
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I have to take my pet grapefruit out.
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I have to weigh it.
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Then I have to just write that down.
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Just doing that I am collecting data,
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so you could argue that
maybe I'm kinda starting
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to mess with statistics a little bit,
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but I'm just getting one data point.
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So I might weigh it and I might see
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my grapefruit weighs one pound,
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but that's not data with variability.
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That's just one data point.
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In order to have
variability you have to have
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multiple data points
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and should be at least
possible that they could vary.
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So, for example, all of
these folks ate zero bricks
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but maybe it was possible that
someone actually ate a brick.
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But here I have just one data point.
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With one data point, you
can't have variability,
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so this is not a statistical question.
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I just collect a data point.
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Next question, what is the average number
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of cars in a parking
lot on Monday mornings?
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To think about whether it
is a statistical question,
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we just have to think about
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what do I have to do to
answer that question?
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I would have to go out to the parking lot
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on multiple Monday mornings,
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and measure the number of cars.
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So on the first Monday morning
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I might see there are 50 cars.
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The next Monday morning
I might go out there
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and count there's 49 cars.
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The next Monday morning I
might see 50 cars again.
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The next Monday morning
I might see 63 cars.
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So I'm collecting multiple data points
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to answer this question.
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Then I'm going to take
the average of all these,
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but I'm collecting multiple data points
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to answer this question.
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It's definitely possible that
there could be variation here,
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that there could be variability,
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so this is a statistical question.
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Next question, am I hungry?
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It's an important question.
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We ask it to ourselves multiple times.
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In fact, sometimes our
bodies just tell it to us.
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But I am definitely not collecting ...
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I guess you could say I'm collecting
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some type of feelings from my stomach
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or how weak I feel or not,
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but it's definitely not
data with variability.
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I'm either hungry or not
hungry on a given day.
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I mean if you said broader,
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how does my hunger change from day to day
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and you came up some type of a
scale for rating your hunger,
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all right maybe that's more statistical.
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But just am I hungry, a yes-no question.
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This is not ...
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To answer this I do not have to
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collect data with variability,
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so this is not a statistical question.
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How many teeth does my mother have?
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To do this I would have
to go find my mother,
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and then I would have to
ask her to open her mouth,
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and count the teeth in her mouth.
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Maybe I'd get a number like 30.
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So it's kind of like how much
does my pet grapefruit weigh.
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I do have to collect one data point,
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but one data point is not
going to have variability,
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so I am not collecting
data with variability,
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so this is not a statistical question.
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If I said how many teeth
do all of the mothers
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that I know have on average,
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or what's the range of number of teeth
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of the mothers I know have,
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that would be statistical.
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But this is just one data
point, so not statistical.
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How much time do the members of my family
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spend eating per year?
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Once again, what do I need to
do to answer this question?
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I would have to go either observe
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or survey my family members,
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maybe my mom, my wife, my children,
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and my uncles, aunts, whoever else,
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and I would say how much
do you eat each day?
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I would add them all up to figure out
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how much they eat in a year.
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Maybe family member A
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eats 813 hours in a year.
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Family member B ate, I don't know,
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732 hours in the year.
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So you see the general notion
that I will be collecting
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multiple data points from
the different family members.
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There very well, and in fact,
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there's very likely to
be variation in that.
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In fact, I might even see
variation from year to year.
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Person A is probably going to eat
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a different number of
hours in the next year.
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So I'm definitely going to
collect data with variability
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in order to answer this question.
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So that is a statistical question.
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Then finally, I have the question,
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how many times have I watched Star Wars?
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This is very similar to how
many teeth does my mother have,
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or how much does my pet grapefruit weigh.
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I just have to count the number of times
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that I watched Star Wars.
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Maybe I watched it seven times.
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Just one data point.
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No variability here.
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If I said on average how many times
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have my co-workers watched Star Wars,
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then I'm gonna have to
collect data with variability.
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I'm gonna collect multiple data points,
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and it's definitely
possible that my co-workers
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have watched it different
numbers of times.
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But for this question in particular,
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where it's just one
data point to answer it,
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how many times have I watched Star Wars?
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My answer in this case
actually I think is seven.
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Then not a statistical question.
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So hopefully that gives you a sense
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of statistics variability
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and what a statistical question even is.
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