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  • 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 the 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 and their 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 2, 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 its

  • 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 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 5 and a mode of 6.

  • As the mean is lower than the median, we say that there is a negative or left skew.

  • Once again, the highest point is defined by the mode.

  • Why is it called a left skew, again?

  • That’s right, because the outliers are to the left.

  • Alright.

  • 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 dataset.

  • 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.

The most commonly used tool to measure asymmetry is skewness.

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