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In this segment, we want
to reinforce the message

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that how you choose to sample
can give different results,

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and the choice of
sampling is important.

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Suppose you're interested in
measuring the average family

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size in some population.

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Suppose that there are
families that are small

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and have just one
person in them,

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and there's also a family
that has many people in it.

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What does it mean to measure
the average family size?

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One possibility is to pick at
random a family, each family

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being chosen with
equal probability,

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and talk about the expected
value that you get,

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or the average value
if you sample that way.

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In this particular example
with probability 1/4,

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you get a 1, with
probability 1/4, you get a 1

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with probability
1/4, you get a 1.

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So the answer would be with
probability 3/4 you get a 1,

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and with probability
1/4, you get a 6.

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But suppose that instead,
you pick a person at random

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and you ask for that person,
how big is your family?

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What's the expected value of
the answer you're going to get?

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Here we have nine people.

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Out of those nine
people, 3 of them

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will give you an answer
my family has size one,

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and six of those people
will give you an answer,

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my family has a size of six.

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And this number is
going to be larger

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than the previous number.

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You're going to get
different answers.

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So it is possible to
have a situation where

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you can make a statement
such as the following.

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The average family
size is three,

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but the average person lives
in a family of size four.

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There is no contradiction
between these two statements

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because we're measuring
different things.

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Another example of
the same flavor.

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You're interested in the
average bus occupancy.

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You're interested in whether
buses are crowded or not

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in your city.

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One way of carrying
out this calculation

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is to pick buses
at random, each bus

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is equally likely to
be picked, and see

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how many people are
riding this bus.

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Another possibility is to
take a typical passenger,

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a random passenger, and ask
them, how crowded was your bus?

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Take an extreme case.

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Suppose that half of the
buses have 0 people in them,

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and half of the buses
have 50 people in them.

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If you look at random buses,
then the average occupancy

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would be 25.

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But if you ask passengers,
all of the passengers

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would report 50, and it would
be, again, a different answer.

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A similar situation is if you're
talking about average class

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sizes.

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One method is to look
at all the classes,

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see how many students
there are in each class,

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and take the average.

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Another method would be
to ask a typical student,

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how large is your class?

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Because more students are
in large classes, when

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you pick a student
at random, you

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are likely to get a
higher answer, as opposed

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to when you look
at a random class.

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The moral from
all these examples

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is that it is very
important to be

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careful about what
you choose to sample.

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When you pick at
random, what exactly

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are you picking at random?

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And you need to be aware
that different sampling

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methods measure
different things,

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and will generally give
you different results.