Univariate Measures: Asymmetry

00:00 After exploring the measures of central tendency.

00:03 Let's move on to the measures of asymmetry.

00:06 The most commonly used tool to measure asymmetry is skewness.

00:10 This is the formula to calculate it.

00:14 Almost always, you will use software that performs the calculation for you.

00:18 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.

00:30 Skewness can be confusing at the beginning, so an example is in place.

00:36 Remember frequency distribution tables from previous lectures.

00:39 Here we have three data sets and their respective frequency distributions.

00:44 We have also calculated the means, medians and modes.

00:48 The first data set has a mean of 2.79 and a median of two.

00:53 Hence, the mean is bigger than the median.

00:56 We say that this is a positive or right skew.

01:00 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.

01:07 It does not depend on which side the line is leaning to, but rather to which side its tail is leaning to.

01:13 So right skewness means that the outliers are to the right.

01:19 It is interesting to see the measures of central tendency incorporated in the graph when we have right skewness.

01:25 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.

01:37 The frequency of occurrence is completely symmetrical, and we call this a zero or no skew. Most often, you will 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.

01:54 As the mean is lower than the median.

01:57 We say that there is a negative or a left skew.

02:00 Once again, the highest point is defined by the mode.

02:04 Why is it called a left SKU again? That's right. Because the outliers are to the left.

02:11 All right. So why is skewness important? Skewness tells us a lot about where the data is situated.

02:18 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.

02:25 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.

02:36 Thanks for watching.