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Dispersion, which is
also called variability,

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scatter or spread, is
the extent to which

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the data distribution is
stretched or squeezed.

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The common measures of

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dispersion are standard
deviation and variance.

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If you are at a
university or college,

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you may have heard
about the bell curve,

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which looks like this.

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You will often hear
this is within

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one standard deviation
of the mean or

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within two standard
deviations of the mean.

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Let's see what that means.

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Let's look at the age
of an instructor.

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Let's say the average age is 52.

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This means that the
individual ages may differ,

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some may be 48 or maybe 55 or 75.

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So the average age
is an estimate.

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But what we also need is

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an estimate for the
dispersion in the data-set.

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The other thing to note is
the range in our data-set.

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For example, the difference
of the ranges from a minimum

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of 29 years of age to
a maximum of 73 years.

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This to you refers
to a distance or

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the difference between the
minimum and the maximum.

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Unlike the difference between
population and sample mean,

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the difference between
a variance for

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the population and a sample is

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that when you compute
the population variance

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denoted as sigma squared,

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you divide it by the total
number of observations.

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These are the deviations between

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observation and the mean squared,

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then added and then divided by

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the total number of observations.

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For sample variance, which
is denoted as S squared,

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you divide it by N minus 1.

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The purpose of using
N minus 1 is so

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that our estimate is
unbiased in the long run.

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That means if we take
a second sample,

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we'll get a different
value of S squared.

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If we take a third sample,

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we'll get a third value
of S squared and so on.

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We use N minus 1 so
that the average of

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all these values of S squared
is equal to sigma squared.

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We usually talk
about squares called

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standard deviation rather
than the variance.

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Standard deviation is
essentially the square root of

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the variance or the
variances in square units.

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It's good to use the
standard deviation because

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it's exactly the same
units as the variable.

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The standard deviation
of age will also

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be measured in years
rather than years squared.

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Here you see that we just
took the square root of

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variance and this becomes
standard deviation.

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We'll return to our
data-set and we'll

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look at the variables
that we computed before.

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You can see that the
standard deviation

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for beauty, evaluation scores,

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and age were computed with

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the descriptive statistics using

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the describe function in Python.

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Let me explain why mean and

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standard deviation have
to go hand in hand.

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I will use the example from

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basketball about the two giants,

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Michael Jordan and
Wilt Chamberlain,

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who preceded Michael Jordan.

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If you consider their
average score per game,

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you would notice that
they didn't differ much.

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Their average was
around 30 points

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for both Jordan and Chamberlain.

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However, when you look at

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the standard deviation
of their performance,

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Jordan was around
4.76 compared to

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Chamberlain who was
at around 10.59.

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If you were to plot this
distribution to see

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Michael Jordan scores using

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the mean and standard deviation.

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Assuming that their scores
are normally distributed.

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You would notice even though

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both players had
around the same mean,

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the tighter distribution
for Jordan suggests that he

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was more consistent in his
performance than Chamberlain.

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The main takeaway is that

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average will only paint
a partial picture.

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If you really want to understand

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the complete picture about
a variable or data-set,

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it is important to compute
both the average and

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the standard deviation to get

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insights on what the
data is telling us.

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So a mean with a
standard deviation means

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something more useful
than the mean by itself.