Original subtitles

Narrator: Okay, excellent.

We already know how to create graphs

and tables for categorical variables.

In this lesson, we are going to do the same

for numerical variables and given that numerical data

is the main focus of this course,

we will spend a couple of lessons on this topic.

Whenever we wanna plot data, it is best to first order it

in a table, so as we did with categorical variables,

let's start by creating a frequency distribution table.

Here's a list of 20 different numbers.

If we arranged them in a frequency table

like the one we use for categorical variables,

we would obtain a table with 20 rows,

each of them representing one number

with a corresponding frequency of one

as each number occurs exactly one time.

This table would be impractical for any analysis, right?

Well, when we deal with numerical variables,

it makes much more sense to group the data into intervals

and then find the corresponding frequencies.

In this way, we make a summary of the data that allows

for a meaningful visual representation.

How do we choose these intervals?

Generally, statisticians prefer working with groups of data

that contain five to 20 intervals.

This way, the summary can be useful.

However, this varies from case to case

and the correct choice of intervals largely depends

on the amount of data we are working with.

In our example, we will divide the data

into five intervals of equal length.

A simple formula that we use is as follows.

The interval width is equal to the largest number

minus the smallest number divided

by the number of desired intervals.

In our case, the length of the interval

should be 100 minus one divided by five.

The result is 19.8.

Now we wanna round this number up

in order to reach a neater representation.

Therefore, our intervals will be as follows, one to 21,

21 to 41, 41 to 61, 61 to 81, and 81 to 101.

Each interval has a width of 20.

Okay.

Let's try to construct the frequency distribution table.

A number is included in a particular interval

if that number is greater than the lowest bound

and equal to or less than the largest bound.

As we can see from the table,

there are two numbers in the first interval,

four in the second, three in the third, six in the fourth,

and five in the fifth interval.

For many analyses, it is useful to calculate

the relative frequency of the data points in each interval.

As we said in a previous video,

the relative frequency is the frequency

of a given interval as part of the total.

Let's add another column to our table

and name it relative frequency.

So the interval from one to 21 has an absolute frequency

of two, but a relative frequency of two divided

by the number of 20 numbers which gives us 10%

and so on until we fill the table.

All right!

This is how we calculate relative frequencies.

Now that we have summarized the raw data,

we can start plotting it.