Original subtitles

-: This lesson will introduce you to

the three measures of central tendency.

Don't be scared by the terminology,

we are talking about mean, median, and mode.

Even if you are familiar with these terms,

please stick around as we will explore their

upsides and shortfalls.

Ready?

Lets go.

The first measure we will study is the mean,

also know as the simple average.

It is denoted by the Greek letter MU for a population

and x bar for a sample.

These notions will come in handy in the next section.

We can find the mean of a data set by adding up all of it's

components and then dividing them by their number.

The mean is the most common measure of central tendency,

but it has a huge downside.

It is easily affected by outliers.

Let's aid ourselves with an example.

These are the prices of pizza at eleven different locations

in New York City and ten different locations in LA.

Let's calculate the mean's of

the two data sets using the formula.

For the mean in NYC, we get eleven dollars.

Whereas for LA, just 5.5.

On average, pizza in New York can't be

twice as expensive as in LA, right?

Correct!

The problem is that in our sample,

we included one posh place in New York

where they charge 66 dollars for pizza

and this doubled the mean.

What we should take away from this example

is that the mean is not enough to make definite conclusions.

So, how can we protect ourselves from this issue?

You guessed it!

We can calculate the second measure, the median.

The median is basically the middle number

in an ordered data set.

Let's see how it works for our example.

In order to calculate the median we have to

order our data in ascending order.

The median of the data set is the number at position

n + 1 divided by 2 in the ordered list,

where n is the number of observations.

Therefore, the median for NYC is at the

sixth position, or six dollars.

Much closer to the observed prices

than the mean of eleven dollars, right?

What about LA?

We have just ten observations in LA.

According to our formula, the median is at positions 5.5.

In cases like this, the median is the simple average

of the numbers at position 5 and 6.

Therefore, the median of LA prices is 5.5 dollars.

Okay, we have seen that the median

is not affected by extreme prices.

Which is good when we have posh New York restaurants

and a street pizza sample.

But, we still don't get the full picture.

We must introduce another measure, the mode.

The mode is the value that occurs most often.

It can be used for both numerical and categorical data,

but we will stick to our numerical example.

After counting the frequencies of each value,

we find that the mode of New York pizza

prices is three dollars.

Now, that's interesting.

The most common price of pizza in NYC is just 3 dollars,

but the mean and median led us to

believe it was much more expensive.

Okay,

let's do the same and find the mode of LA pizza prices.

Hm, each price only appears once.

How do we find the mode then?

Well, we say there is no mode.

But, can't I say there are ten modes, you may ask?

Sure you can,

but it will be meaningless with ten observations

and experienced datatician would never do that.

In general you often have multiple modes.

Usually, two or three modes are tolerable,

but more than that would defeat the

purpose of finding a mode.

There is one last question we haven't answered.

Which measure is best?

The NYC and LA example shows us that the measures

of central tendency should be used together,

rather than independently.

Therefore, there is no best,

but using only one is definitely the worst!

All right, now you know about the mean, median, and mode.

In our next video we will use that knowledge

to talk about skewness.

Stay tuned and thanks for watching!