what is skewness 
skewness is the degree of asymmetry observed in a probability distribution when data points on a bell curve are not distributed symmetrically to the left and right sides of the median the bell curve is skewed distributions can be positive and right skewed or negative and left skewed a normal distribution exhibits zero skewness investopedia theresa chiechitypes of skewsnegative or left skewed refers to a longer or fatter tail on the left side of the distribution while positive or right skewed refers to a longer or fatter tail on the right these two skews show the direction or weight of the distribution the three probability distributions below are right skewed to an increasing degree the mean of positively skewed data will be greater than the median in a left skewed distribution the mean of negatively skewed data will be less than the median a right skewed or positive distribution means its tail is more pronounced on the right side than on the left since the distribution is positive the assumption is that its value is positive as such most of the values end up left of the mean this means that the most extreme values are on the right side negative or left skewed means the tail is more pronounced on the left rather than the right most values are found on the right side of the mean in negative skewness as such the most extreme values are found further to the left a zero skew means the data graph is symmetrical and reveals a normal data distribution regardless of how long or fat the distribution tails are measuring skewnesstwo methods to measure skewness include pearson s first and second coefficients of skewness pearson s first coefficient of skewness or pearson mode skewness subtracts the mode from the mean and divides the difference by the standard deviation pearson s second coefficient of skewness or pearson median skewness subtracts the median from the mean multiplies the difference by three and divides the product by the standard deviation s k 1 x m o s s k 2 3 x m d s where s k 1 pearson s first coefficient of skewness and s k 2 the second s the standard deviation for the sample x is the mean value m o the modal mode value m d is the median value begin aligned qquad qquad qquad quad frac sk 1 frac bar x mo s sk 2 frac 3 x md s textbf where sk 1 text pearson s first coefficient of skewness and sk 2 qquad quad text the second s text the standard deviation for the sample bar x text is the mean value mo text the modal mode value md text is the median value end aligned sk2 s3 x md sk1 sx mo where sk1 pearson s first coefficient of skewness and sk2 the seconds the standard deviation for the samplex is the mean valuemo the modal mode valuemd is the median value pearson s first coefficient of skewness is used if the data exhibit a strong mode pearson s second coefficient may be preferable if the data have a weak mode or multiple modes as it does not rely on mode as a measure of central tendency skewness tells you where the outliers occur although it doesn t tell you how many outliers occur 