Original subtitles

-: So far we have covered graphs

that represent only one variable.

But how do we represent relationships between two variables?

In this video, we'll explore cross tables and scatter plots.

Once again, we have a division

between categorical and numerical variables.

Let's start with categorical variables.

The most common way to represent them is using cross tables

or as some statisticians call them contingency tables.

Imagine you are an investment manager

and you manage stocks, bonds

and real estate investments for three different investors.

Each of them has a different idea of risk, and hence

their money is allocated in a different way

among the three asset classes.

A cross table representing all the data looks

in the following way.

You can clearly see the row showing the type

of investment that's been made

and the columns with each investor's allocation.

It is a good practice to calculate the totals

of each row and column as it is often useful

in further analysis.

Notice that the subtotals of the rows give us

total investments in stocks, bonds and real estate.

On the other hand, the subtotals

of the columns give us the holdings of each investor.

Once we have created a cross table

we can proceed by visualizing the data onto a plane.

A very useful chart in such cases is a variation

of the bar chart called the side by side bar chart.

It represents the holdings of each investor

in the different types of assets.

Stocks are in green, bonds are in red

and real estate is in blue.

The name of this type of chart comes

from the fact that for each investor,

the categories of assets are represented side by side.

In this way, we can easily compare asset holdings

for a specific investor or among investors.

Easy, right?

All graphs are very easy to create and read

once you have identified the type of data you are

dealing with and decided on the best way to visualize it.

Finally, we would like to conclude with a very

important graph, the scatter plot.

It is used when representing two numerical variables.

For this example, we have gathered the reading

and writing SAT scores of 100 individuals.

Let me first show you the graph before analyzing it.

All right.

First, SAT scores by component range from 200 to

800 points, and that is why our data is bounded

within the range of 200 to 800.

Second, our vertical access shows the writing scores

while the horizontal axis contains reading scores.

Third, there are 100 students, and the results correspond

to a specific point on the graph.

Each point gives us information about

a particular student's performance.

For example, this is Jane.

She scored 300 on writing, but 550 on the reading part.

Scatter plots usually represent lots

and lots of observations.

When interpreting a scatter plot,

a statistician is not expected to look

into single data points.

He would be much more interested

in getting the main idea of how the data is distributed.

Okay, the first thing we see is

that there is an obvious up trend.

This is because lower writing scores are usually obtained

by students with lower reading scores

and higher writing scores have been achieved

by students with higher reading scores.

This is logical, right?

Students are more likely to do well

on both because the two tasks are closely related.

Second, we notice a concentration of students in the middle

of the graph with scores in the region

of 450 to 550 on both reading and writing.

Remember we said that scores can be

anywhere between 200 and 800?

Well, 500 is the average score one can get

so it makes sense that a lot of people fall into that area.

Third, there is this group of people

with both very high writing and reading scores.

The exceptional students tend to be excellent

at both components.

This is less true for bad students,

as their performance tends to

deviate when performing different tasks.

Finally, we have Jane from a minute ago.

She is far away from every other observation as she scored

above average on reading, but poorly on writing.

This observation is called an outlier

as it goes against the logic of the whole data set.

We will learn more about outliers and how to treat them

in our analysis later on in this course.

So we have gone through the basics.

We have covered populations, samples,

types of variables, graphs and tables.

And it is time for us to dive into

the heart of descriptive statistics,

measurements of central tendency and variability.

Thanks for watching.