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MARK HARTMAN: See,
there's no pattern.

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But what we do want
to say is the top

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shows a large range around
50%, and the bottom--

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boy, even that one sucks--

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the bottom line shows a
smaller range around 50%.

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AUDIENCE: [INAUDIBLE]

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MARK HARTMAN:
Yeah, over the top.

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Top shows a large
range around 50%.

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And I guess I'm not saying
that it's around 50%.

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But it's not that at
75% to 25%, it's 50%.

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But on average, it's still
showing an average of 50%.

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But the spread of our
measurements is pretty wide.

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It goes up to 75%
and down to 25%.

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So the top shows a large
range or spread around 50%.

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The bottom line shows a smaller
range or a smaller spread

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around 50%.

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Has anybody ever heard of
this statistical measurement

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called a standard deviation?

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Probably not.

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That's a mathematical
way of saying

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the average of these values
is if you add them all up

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and divide by the total number.

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It's kind of like
the average value.

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The standard deviation
is a way of measuring

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how much do your values spread
around that central value,

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around that average value.

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So this is the observation
that we're seeing.

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What was different
about the first line

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versus the last line over here?

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Nicki?

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AUDIENCE: More tosses.

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MARK HARTMAN: We
had more tosses.

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So I'm just going to
fill you in on what

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we say this model--
what is the model

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to explain this observation.

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The model is that
repeated measurements--

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when we say repeated
measurements--

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wait a minute.

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I want to say this
the right way.

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Right.

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No, OK.

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So the model is if we have a
repeated measurement, repeated

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measurements are closer
to the actual value.

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If we do more
measurements of something,

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we're more likely to have
our answer be close to what

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the actual value is.

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Now, this happens with things
that have probabilities,

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like flipping coins, as
well as collecting photons.

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Because if you took a
picture of an object

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and you collected a
certain number of photons,

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say, in five seconds, and
then you collected photons

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in another five seconds, even
if it was the same object, even

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if it was giving off the
same amount of luminosity,

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you're going to collect a
slightly different number

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of photons.

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Let's summarize a
little bit, and then

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I'm going to ask you guys a
couple of questions, I think.

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So let's put down-- so this
is our model, that if we make

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repeated measurements-- and
that means either flipping coins

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more or collecting more photons
in a single bin or more photons

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with our image.

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We want to say that error bars--

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this is kind of
another definition.

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These error bars
or uncertainties

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are an estimate of the
range in which we'd

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find the actual value.

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Because there is a real
measurement of the flux,

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but because we can't measure
everything perfectly well--

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we have to measure only the
photons that we're getting--

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we have to have an
estimate of the range

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where the actual
value would lie.

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So OK, I'll get out of the
way so you guys can write that

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down.

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Error bar is an
estimate of the range

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in which we'd find the
actual, real value,

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just like we saw up here.

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So this measurement
would have a large--

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or let's just say here,
our range of 50% is about--

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our range is 50% from the lowest
value to the highest value.

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Here, our range is 25%.

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Here, our range,
from the lowest value

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to the highest value, 25--

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that's 19%.

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And here, our range is 37
to 56, so that's about 19.

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Is that right--

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37, 47, 57, 19.

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So you can see that
our range gets smaller

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as we make more measurements.

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In the same way, our
error bars get smaller

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as we have more photons.

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We've measured things
multiple times.