Statistics Phase 6-: Skewness

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SKEWNESS
Skewness means lack of symmetry.
Data can be skewed meaning that it tends to have a long tail on one side or the other.
POSITIVE SKEWNESS
Let’s take an example of the number of accident claims by an insurance customer in a sample of 50 people.
NUMBER OF CLAIMS
FREQUENCY
0
30
1
15
2
5
3
3
4
2
5 or more
1
TOTAL
50

Mean=8.33
Mode=0
Median=4
Here we can see that MEAN > MEDIAN
After plotting, this looks like this

From the graph, its clear that there is no symmetry in this as most of the data is concentrated towards the left of the graph and the tail is towards its right. So it is called positively skewed or right skewed.
NEGATIVE SKEWNESS
Lets take an example of 20 students obtaining CGPAs at the end of the semester exams.
CGPA
NO. OF STUDENTS
0-2
0
2-4
1
4-6
5
6-8
6
8-10
8
TOTAL
20

Mean = 4
Median = 5
Mode = 8-10 CGPA
Here, Mean < Median

NO SKEWNESS
When mean=median=mode, there is 0 skewness or it is normally distributed.









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