Original subtitles

-: After exploring the measures of central tendency,

let's move on to the measures of asymmetry.

The most commonly used tool to measure asymmetry

is skewness.

This is the formula to calculate it.

Almost always you will use software that performs

a calculation for you.

So in this lesson, we will not get into the computation

but rather the meaning of skewness.

So skewness indicates whether the observations

in a data set are concentrated on one side.

Skewness can be confusing at the beginning.

So an example is in place.

Remember frequency distribution tables

from previous lectures?

Here we have three data sets,

in the respective frequency distributions.

We have also calculated the means, medians, and modes.

The first data set has a mean of 2.79 and a median of two.

Hence, the mean is bigger than the median.

We say that this is a positive or right skew.

From the graph, you can clearly see

that the data points are concentrated on the left side.

Note that the direction of the skew is counterintuitive.

It does not depend on which side the line is leaning to

but rather to which side it's tail is leaning to.

So right skewness means that the outliers are to the right.

It is interesting to see the measures

of central tendency incorporated in the graph.

When we have right skewness, the mean is bigger

than the median, and the mode is the value

with the highest visual representation.

In the second graph, we have plotted a data set

that has an equal mean, median and mode.

The frequency of occurrence is completely symmetrical

and we call this a zero or a no skew.

Most often you'll hear people say

that the distribution is symmetrical.

For the third data set,

we have a mean of 4.9, a median of five, and a mode of six.

As the mean is lower than the median,

we say that there is a negative or a left skew.

Once again, the highest point is define by the mode.

Why is it called a left skew again?

That's right, because the outliers are to the left.

All right, so why is skewness important?

Skewness tells us a lot about where the data is situated.

As we mentioned in our previous lesson,

the mean, median and mode

should be used together to get a good understanding

of the data set.

Measures of asymmetry like skewness are the link

between central tendency measures and probability theory

which ultimately allows us to get a more complete

understanding of the data we are working with.

Thanks for watching.