Original subtitles

Narrator: While variance is a common measure

of data dispersion in most cases,

the figure you will obtain is pretty large

and hard to compare as the unit of measurement is squared.

The easy fix is to calculate it square root

and obtain a statistic known as standard deviation.

In most analyses, you perform standard deviation

will be much more meaningful than variants.

As we saw in the previous lecture.

There are different measures

for the population and sample variants.

Consequently, there is also population

and sample standard deviation.

The formulas are the square root of the population variance

and square root of the sample variance, respectively.

I believe there is no need

for an example of the calculation, right?

If you have a calculator in your hands

you'll be able to do the job.

All right?

The other measure we still have to introduce is

the coefficient of variation.

It is equal to the standard deviation divided by the mean.

Another name for the term is relative standard deviation.

This is an easy way to remember its formula.

It is simply the standard deviation relative to the mean.

As you probably guessed

there is a population and sample formula once again

so standard deviation is the most common measure

of variability for a single data set.

But why do we need yet another measure such

as the coefficient of variation?

Well, comparing the standard deviations

of two different data sets is meaningless

but comparing coefficients of variation is not.

Aristotle once said, Tell me, I'll forget.

Show me, I'll remember.

Involve me, I'll understand.

To make sure you remember, here's an example

of a comparison between standard deviations.

Let's take the prices of pizza at 10 different places

in New York, they range from one to $11.

Now, imagine that you only have Mexican pesos, and to you

the prices look more like 18.81 pesos to 206.91 pesos.

Given the exchange rate of 18.81 pesos for $1

let's combine our knowledge so far and find the standard

deviations and coefficients of variation

of these two data sets.

First, we have to see if this is a sample or a population.

Are there only 11 restaurants in New York?

Of course not.

This is obviously a sample drawn from all the restaurants

in the city.

Then we have to use the formulas for sample measures

of variability.

Second, we have to find the mean.

The mean in dollars is equal to 5.5 and the mean in pesos

to 103.46.

The third step of the process

is finding the sample variance.

Following the formula that we showed earlier

we can obtain $10.72 squared and 3793.69 peso squared.

The respect of sample standard deviations

are $3.27 and 61.59 pesos.

Let's make a couple of observations.

First, variance gives results

in squared units while standard deviation in original units.

This is the main reason why professionals prefer to

use standard deviation as the main measure of variability.

It is directly interpretable.

Square dollars means nothing even

in the field of statistics.

Second, we got standard deviations of 3.27

and 61.59 for the same pizza

at the same 11 restaurants in New York City.

Seems wrong, right?

Don't worry.

It is time to use our last tool

the coefficient of variation

dividing the standard deviations by the respective means.

We get the two coefficients of variation.

The result is the same, 0.60.

Notice that it is not dollars pesos, dollars squared

or peso squared.

It is just zero point 60.

This shows us the great advantage

that the coefficient of variation gives us.

Now, we can confidently say

that the two data sets have the same variability

which is what we expected beforehand.

Let's recap what we have learned so far.

There are three main measures of variability,

variance, standard deviation and coefficient of variation.

Each of them has different strengths and applications.

You should feel confident using all of them

as we are getting closer to more complex statistical topics.

And remember, Aristotle's advice,

involve me, I'll understand.

So please don't forget to get involved with the exercises.