Statistics Skewness

Statistics Skewness 

Skewness Statistics, Skewness is an asymmetry in the distribution of a sample data. When a sample data is graphically displayed, some distributions of the data have more observations on one side of the graph than the other side, this is called skewness. There are right and left skewness.  Distributions in which most of the observations are on the left that is towards the lower values, the skewness is said to be skewed right; and if the distribution in which most of the observations are on the right that is towards the higher values, the skewness is said to be skewed left. So, skewness statistic or skewness is the measure of symmetry or otherwise the lack of symmetry. A distribution when displayed on a graph is said to be symmetric if it looks the same to the right and left of a vertical line drawn in the centre point, just like mirror images.

Skewness in Statistics: In statistics, many statistical analyses fundamental task is to characterize the location and variability of a set of data. Skewness is one of the further characterizations of a data set. Skewness is the measure of symmetry of a frequency distribution of a data set. A sample data with symmetric distribution when graphically displayed shows a ‘hump’ like curve in the middle of the distribution and a tail type of lines on either side. The skewness in such cases is said to be zero. When distributions with large number of frequency scores are seen at the lower end of the distribution which have a tail like line pointing towards higher values and a ‘hump’ like curve over the smaller values; the skewness is said to be positive or the distribution is skewed right. When the distribution with large number of frequency scores are seen at the higher end of the distribution which have a tail like line point towards lower values and a ‘hump’ like curve over the higher values; the skewness is said to be negative or the distribution is skewed left.

Definition of Skewness : Skewness can be defined as the degree to which a statistical distribution is asymmetrical around the mean. In a perfectly symmetric distribution, the skewness is zero.  Distributions that have extreme values or outliners above the mean are said to be positively skewed or skewed right. Distributions that have extreme values or outlines below the mean are said to be negatively skewed or skewed left. In a given data with single variable, we can calculate skewness which is the sum of the deviations from the mean, raised to the third power, divided by number of data items minus 1, times the standard deviation raised to the third power.