Skewness

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In Statistics Skewness is refers to the extent the data is asymmetrical from the normal distribution. Skewness can come in the form of negative skewness or positive skewness, depending on whether data points are skewed to the left and negative.

  1. Positive Skewness: A positively skewed distribution is characterized by many outliers in the upper region, or right tail. A positively skewed distribution is said to be skewed right because of its relatively long upper (right) tail.

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  1. Negative Skewness: A negatively skewed distribution has a disproportionately large amount of outliers that fall within its lower (left) tail. A negatively skewed distribution is said to be skewed left because of its long lower tail.

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Skewness affects the location of the mean, median, and mode of a distribution:

  1. For a symmetrical or normal distribution, the mean, median, and mode are equal.
  1. For a positively skewed, unimodal distribution, the mode is less than the median, which is less than the mean. The mean is affected by outliers; in a positively skewed distribution, there are large positive outliers that tend to “pull” the mean upward, or more positive.
  1. For a negatively skewed, unimodal distribution, the mean is less than the median, which is less than the mode. In this case, there are large, negative outliers that tend to “pull” the mean downward (to the left).

The key to remembering how measures of central tendency are affected by skewed data is to recognize that skew affects the mean more than the median and mode, and the mean is “pulled” in the direction of the skew. Note the median is between the other two measures for positively or negatively skewed distributions.

 

 

 

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