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-: After exploring the measures of central tendency,
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let's move on to the measures of asymmetry.
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The most commonly used tool to measure asymmetry
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is skewness.
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This is the formula to calculate it.
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Almost always you will use software that performs
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a calculation for you.
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So in this lesson, we will not get into the computation
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but rather the meaning of skewness.
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So skewness indicates whether the observations
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in a data set are concentrated on one side.
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Skewness can be confusing at the beginning.
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So an example is in place.
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Remember frequency distribution tables
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from previous lectures?
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Here we have three data sets,
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in the respective frequency distributions.
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We have also calculated the means, medians, and modes.
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The first data set has a mean of 2.79 and a median of two.
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Hence, the mean is bigger than the median.
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We say that this is a positive or right skew.
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From the graph, you can clearly see
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that the data points are concentrated on the left side.
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Note that the direction of the skew is counterintuitive.
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It does not depend on which side the line is leaning to
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but rather to which side it's tail is leaning to.
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So right skewness means that the outliers are to the right.
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It is interesting to see the measures
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of central tendency incorporated in the graph.
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When we have right skewness, the mean is bigger
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than the median, and the mode is the value
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with the highest visual representation.
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In the second graph, we have plotted a data set
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that has an equal mean, median and mode.
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The frequency of occurrence is completely symmetrical
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and we call this a zero or a no skew.
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Most often you'll hear people say
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that the distribution is symmetrical.
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For the third data set,
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we have a mean of 4.9, a median of five, and a mode of six.
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As the mean is lower than the median,
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we say that there is a negative or a left skew.
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Once again, the highest point is define by the mode.
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Why is it called a left skew again?
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That's right, because the outliers are to the left.
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All right, so why is skewness important?
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Skewness tells us a lot about where the data is situated.
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As we mentioned in our previous lesson,
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the mean, median and mode
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should be used together to get a good understanding
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of the data set.
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Measures of asymmetry like skewness are the link
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between central tendency measures and probability theory
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which ultimately allows us to get a more complete
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understanding of the data we are working with.
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Thanks for watching.
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