Statistics Phase 6: Skewness
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

02

0

24

1

46

5

68

6

810

8

TOTAL

20

Mean =
4
Median
= 5
Mode =
810 CGPA
Here,
Mean < Median
NO SKEWNESS
When mean=median=mode,
there is 0 skewness or it is normally distributed.
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