A data set exhibits positive skewness (or is "skewed right") if its histogram has a single peak and the values of the data extend much farther to the right than to the left of the peak. The following histogram describes the family income (in thousands of dollars) of Smalltown's residents. A data set exhibits negative skewness (or is "skewed left") if its histogram has a single peak and the values of the data extend much farther to the left than to the right of the peak. The following histogram shows the number days from conception to birth for babies born at Smalltown Hospital. If the data you are analyzing are not skewed, use the mean as the measure of central tendency. In cases of great skewness, use the median as the measure of central tendency to avoid distortion by extreme values. You can usually assess skewness by simply eyeballing a histogram. To be precise about measuring skewness, apply the Excel SKEW function to a data set. * If SKEW > +1, the data are positively skewed and the median is the better measure of central tendency. * If SKEW < -1, the data are negatively skewed and the median is again the better measure of central tendency. * If SKEW is between -1 and +1, the data are relatively symmetric and the mean is the better measure of central tende Please download file Skewness.xlsx. Let's compare the mean and the median as measures of central tendency for the IQ, income, and conception-to-birth data sets. In the cell range D3:F3, the skewness for each data set has been computed — e.g., using the formula =SKEW(F8:F657) for IQs in cell D3. The median, mode, and mean for each data set have been computed using the MEDIAN, MODE, and AVERAGE functions, respectively. For positively skewed data sets, the mean is greater than the median. For negatively skewed data sets, the mean is less than the median. For relatively symmetric data sets, the mean and median are usually very close in value. The three example data sets are consistent with these...

...Skewness, Kurtosis, and the Normal Curve
Skewness
In everyday language, the terms “skewed” and “askew” are used to refer to something that is out of line or distorted on one side. When referring to the shape of frequency or probability distributions, “skewness” refers to asymmetry of the distribution. A distribution with an asymmetric tail extending out to the right is referred to as “positively skewed” or “skewed to the right,” while a distribution with an asymmetric tail extending out to the left is referred to as “negatively skewed” or “skewed to the left.” Skewness can range from minus infinity to positive infinity.
Karl Pearson (1895) first suggested measuring skewness by standardizing the difference between the mean and the mode, that is, . Population modes are not well estimated from sample modes, but one can estimate the difference between the mean and the mode as being three times the difference between the mean and the median (Stuart & Ord, 1994), leading to the following estimate of skewness: . Many statisticians use this measure but with the ‘3’ eliminated, that is, . This statistic ranges from -1 to +1. Absolute values above 0.2 indicate great skewness (Hildebrand, 1986).
Skewness has also been defined with respect to the third moment about the mean: , which is simply the expected value of the distribution of cubed z scores....