Some distributions of data, such as the bell curve or normal distribution , are symmetric. This means that the right and the left of the distribution are perfect mirror images of one another. Not every distribution of data is symmetric. Sets of data that are not symmetric are said to be asymmetric. The measure of how asymmetric a distribution can be is called skewness.
The mean, median and mode are all measures of the center of a set of data. The skewness of the data can be determined by how these quantities are related to one another. Data that are skewed to the right have a long tail that extends to the right. An alternate way of talking about a data set skewed to the right is to say that it is positively skewed.
In this situation, the mean and the median are both greater than the mode. As a general rule, most of the time for data skewed to the right, the mean will be greater than the median. In summary, for a data set skewed to the right:. The situation reverses itself when we deal with data skewed to the left. Data that are skewed to the left have a long tail that extends to the left. An alternate way of talking about a data set skewed to the left is to say that it is negatively skewed.
In this situation, the mean and the median are both less than the mode. As a general rule, most of the time for data skewed to the left, the mean will be less than the median. In summary, for a data set skewed to the left:. It can be very subjective to determine which is more skewed by simply looking at the graph of the distribution.
This is why there are ways to numerically calculate the measure of skewness. Many sources use the term kurtosis when they are actually computing "excess kurtosis", so it may not always be clear. The following example shows histograms for 10, random numbers generated from a normal, a double exponential, a Cauchy, and a Weibull distribution. Normal Distribution. The first histogram is a sample from a normal distribution. The normal distribution is a symmetric distribution with well-behaved tails.
This is indicated by the skewness of 0. The kurtosis of 2. The histogram verifies the symmetry. The second histogram is a sample from a double exponential distribution. The double exponential is a symmetric distribution. Compared to the normal, it has a stronger peak, more rapid decay, and heavier tails. That is, we would expect a skewness near zero and a kurtosis higher than 3.
The skewness is 0. The third histogram is a sample from a Cauchy distribution. For better visual comparison with the other data sets, we restricted the histogram of the Cauchy distribution to values between and The full data set for the Cauchy data in fact has a minimum of approximately , and a maximum of approximately 89, The Cauchy distribution is a symmetric distribution with heavy tails and a single peak at the center of the distribution.
Since it is symmetric, we would expect a skewness near zero. Due to the heavier tails, we might expect the kurtosis to be larger than for a normal distribution. In fact the skewness is These extremely high values can be explained by the heavy tails.
Just as the mean and standard deviation can be distorted by extreme values in the tails, so too can the skewness and kurtosis measures. Ask questions; get answers. How to Get a Perfect , by a Perfect Scorer. Score on SAT Math. Score on SAT Reading. Score on SAT Writing. What ACT target score should you be aiming for? How to Get a Perfect 4.
How to Write an Amazing College Essay. A Comprehensive Guide. Choose Your Test. These graphs are called bell curves due to their clearly defined, bell-like shape: On a normal distribution graph, the mean average , median, and mode are all equal.
What Does Skewed Right Mean? Example of a right-skewed histogram. What Causes a Right-Skewed Histogram? Have friends who also need help with test prep? Share this article! Hannah Muniz.
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