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So far we have displayed
data as averages and counts.

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Now let's look at some other
statistical parameters

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that we will illustrate
as graphics.

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We have not yet shown
anything about variance

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and I think the first thing

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that one should look
into beyond averages,

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is to look at variance or how
the data are distributed.

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A good way of looking at
the distribution of data,

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especially if it were to
be a continuous variable,

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is to look at histograms.

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If you are interested in

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displaying something
more than the average,

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maybe the median
and the quartiles,

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then perhaps boxplots
should be our choice.

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Using the teaching
evaluation data,

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we have plotted a histogram

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of teaching evaluation scores.

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You could see that the
mean score is around four,

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but then you could see

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very low teaching evaluation
scores, not many frequently,

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but most frequently is the around

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the average and
then you'd see that

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some have lower teaching
evaluation scores and

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some have fairly high
teaching evaluation scores.

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The histogram approximates the
normal distribution curve.

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Essentially you have 3.99
to four as the mean,

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the standard deviation of 0.55,

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looking at 463 records.

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This gives you a good idea of

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how your data are distributed.

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You can in fact plot

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multiple histograms such that

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you can see the difference
between the subgroups.

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Here you have the histograms

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overlaid for males and females.

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These frequent lower teaching
evaluations for females

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is likely to influence

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the average teaching
evaluation score

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for females versus the males.

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A box plot essentially
looks like this.

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The thick line in the box
represents the median.

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The top part of the box
is the third quartile.

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The bottom part of the box
as the first quartile.

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The line at the bottom
is the minimum value,

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and the line at the top
is the maximum value.

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The range between the
first quartile and

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the third quartile is called
the inter-quartile range.

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In this graphic, we have created

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the box plots for
the age variable.

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We can see that the
median age of males

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is higher than the
median age of females.

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Also, the maximum
age of the males is

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higher than the maximum
age of females.

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To do this in Python,

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we use the boxplot function
in the Seaborne library.

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We will put the gender
on the Y axis and

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the age of the instructor
on the X axis.

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You can play around
with the X and Y axis.

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If you want a horizontal style
boxplot for readability,

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I like to use vertical boxplots.

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We can also add
another dimension.

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Here we will add tenure.

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So those who are tenured
are plotted on the right,

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and those who were not tenured
are plotted on the left.

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The blue color represents
the female instructors,

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and the orange color represents
the male instructors.

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We can see the differences
between male and female.

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Instructors, male
tenured instructors

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are older than male
untenured instructors,

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whereas female tenured
instructors are

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younger than female
untenured instructors.

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To do this in Python,

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add the hue argument at
the box plot function.

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A pie chart is another way
of looking at your data.

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You can see here in

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this graphic that the
number of courses taught by

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male instructors is
larger than the number of

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courses taught by
female instructors.

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To do this in Python,

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we will use the
matplotlib library.

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First we specify the labels,

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get the number of courses taught

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both by male and females,

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and assign it to a
size is variable.

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Create a subplot,
insert the sizes,

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labels and percentage to

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one decimal place in
the pie function,

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and print out the pie chart
with the show function.