Skewness can be defined as the asymmetry in the Distribution of data.The value on one side of the distribution tend to be further more than the “ Middle” than the values on the other side.The Distribution is said to be skewed if the Mean and the Median falls at different points in a distribution. If the balance or centre of gravity is shifted to left then it is called positively skewed and if the balance or centre of gravity shifted to right is called as negatively skewed. Positively Skewed is more common than the negatively skewed.
Skewness Example: In normal condition the distribution will be in Bell shape. Whereas in skewness the distribution yields more either at left or right.Consider the following example:
The monthly wise AC machines sold in a year from January to December are as follows:
30,45,60,70,80,60,40,40,35,35,30,25. The sale affected by climatic conditions. Peak sale is in May i.e.80. Up to May the sale is progressive and from June it is gradually decreased. If we plot a graph the picture will be skewed and represents Positively Skewed Distribution.
Interpreting Skewness: If the distribution is asymmetrical then it is called skewness. If Mean is greater than the mode then the skewness will be positive. If the difference is greater the skewness will be more. The frequencies in the distribution as in the above example say the marks of students in a college is very high marks achieved by maximum students then the graph will be skewed towards left. Then it is called negatively skewed.
• If Skewness is less than -1 or greater than + 1 the distribution can be interpreted as highly skewed.
• If Skewness is in between -1 to -1/2 or 1 to ½ the distribution is moderately skewed.
• If skewness is in between -1/2 to ½ then the distribution is approximately symmetric.
Measure of Skewness: Measure of skewness tells us the asymmetry of direction of frequency distribution. Skewness can be measured in absolute terms by taking the difference between Mean & Mode. There are four important measures of Relative Measure of skewness namely:
• The Karl Pearson’s Coefficient of Skewness
• The Bowley’s Coefficient of Skewness
• The Kelly’s Coefficient of Skewness
• Measure of Skewness based on Moments
Skewness of Data: In a college, the marks scored by the student are as follows:
54,57,63,69,78,83,83,84,84,85,85,85,86,86,86,86,87,87,88,90
The average of marks = Mean = 84.55
Mode = the data value of highest frequency = 86 (4 times repeated)
Absolute Skewness is defined as the difference of Mode and Mean. Mathematically, it can be represented as
Absolute skewness = Mode - Mean
Histogram Skewness: As in the skewness of data, the data can be classified in to class intervals.
Class Interval Frequency
50 - 60 2
60 – 70 2
70 – 80 1
80 – 90 15
