Free Investment Banking Course. Login details for this Free course will be emailed to you. Download Skewness Excel Template. Forgot Password? Article by Madhuri Thakur. Skewness Meaning Skewness describes how much statistical data distribution is asymmetrical from the normal distribution, where distribution is equally divided on each side.
So basically, there are two types — Positive : The distribution is positively skewed Distribution Is Positively Skewed A positively skewed distribution is one in which the mean, median, and mode are all positive rather than negative or zero.
The data distribution is more concentrated on one side of the scale, with a long tail on the right. It works just the opposite if you have big deviations to the right of the mean. The same is true of skewness.
If you have the whole population, then g 1 above is the measure of skewness. But if you have just a sample , you need the sample skewness :. But how highly skewed are they, compared to other data sets? To answer this question, you have to compute the skewness. Begin with the sample size and sample mean. The sample size was given, but it never hurts to check.
Now, with the mean in hand, you can compute the skewness. That would be the skewness if you had data for the whole population. But obviously there are more than male students in the world, or even in almost any school, so what you have here is a sample, not the population. You must compute the sample skewness :. If skewness is positive, the data are positively skewed or skewed right, meaning that the right tail of the distribution is longer than the left.
If skewness is negative, the data are negatively skewed or skewed left, meaning that the left tail is longer. But a skewness of exactly zero is quite unlikely for real-world data, so how can you interpret the skewness number?
Caution : This is an interpretation of the data you actually have. In that case the question is, from the sample skewness, can you conclude anything about the population skewness? To answer that question, see the next section. Your data set is just one sample drawn from a population. Maybe, from ordinary sample variability, your sample is skewed even though the population is symmetric.
But if the sample is skewed too much for random chance to be the explanation, then you can conclude that there is skewness in the population. To answer that, you need to divide the sample skewness G 1 by the standard error of skewness SES to get the test statistic , which measures how many standard errors separate the sample skewness from zero:.
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.
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. 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? The adjustment approaches 1 as N gets large. For reference, the adjustment factor is 1. The skewness for a normal distribution is zero, and any symmetric data should have a skewness near zero. Negative values for the skewness indicate data that are skewed left and positive values for the skewness indicate data that are skewed right.
By skewed left, we mean that the left tail is long relative to the right tail. Similarly, skewed right means that the right tail is long relative to the left tail. If the data are multi-modal, then this may affect the sign of the skewness. Some measurements have a lower bound and are skewed right. For example, in reliability studies, failure times cannot be negative. It should be noted that there are alternative definitions of skewness in the literature. There are many other definitions for skewness that will not be discussed here.
Note that in computing the kurtosis, the standard deviation is computed using N in the denominator rather than N - 1. The kurtosis for a standard normal distribution is three. In addition, with the second definition positive kurtosis indicates a "heavy-tailed" distribution and negative kurtosis indicates a "light tailed" distribution.
Which definition of kurtosis is used is a matter of convention this handbook uses the original definition. When using software to compute the sample kurtosis, you need to be aware of which convention is being followed.
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