Skewness economics

1. G.H PATEL COLLEGE OF ENGINEERING AND TECHNOLOGY
CIVIL ENGINEERING DEPARTMENT
ACADEMIC YEAR : 2017-18
NUMERICAL AND STATISTICAL METHODS -2140606.
GUIDED BY:
Prof. Tejas Jani
(M.Phill –
Mathematics)
Skewness
Prepared By :
Nirav Tank
150110106056
Kishan Thacker
150110106057
Aaditya Thakkar
150110106058
Nitin Trapasiya
150110106059

2. Content
• What is skewness?
• Types of skewness.
• Graphical represantation
• Methods to find skewness.
• Karl Pearson’s Coefficient
• Example with solution.
• Applications.

3. What is skewness?
• Skewness is a measure that refers to the
extent of symmetry or asymmetry in a
distribution.
• Skewness is asymmetry in a statistical
distribution, in which the curve appears
distorted or skewed either to the left or to the
right.
• Skewness can be quantified to define the
extent to which a distribution differs from a
normal distribution.

4. Types of skewness
• Negative skew: If the curve has a longer tail
towards the left, it is said to be negatively
skewed.
• Positively skew: If the curve has a longer tail
towards the left, it is said to be negatively
skewed.

5. Graphical presentation
#As we can see when mode, median
and mode are equal the curve is
symmertrical.
#While when the s is 0.25 the

6. Methods to find skewness
• Karl Pearson’s Coefficient of Skewness.
• Groeneveld & Meeden’s Coefficient.
• Medcouple.
• Bowley’s measure of skewness (Yule’s
Coefficent)

7. Karl Pearson’s Coefficient
• Karl pearson’s coefficient of skewness
(Mode) is denoted by Sk, is given by,
Sk =
𝑀𝑒𝑎𝑛 −𝑀𝑜𝑑𝑒
𝑆𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝑑𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛
• Karl pearson’s coefficient of skewness
(Median) is denoted by Sk, is given by,
Sk =
3(𝑀𝑒𝑎𝑛 −𝑀𝑒𝑑𝑖𝑎𝑛)
𝑆𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝐷𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛

8. Example
# Calculate Karl Pearson’s coefficient of
skewness for the following data:
X 0 1 2 3 4 5 6 7
Y 12 17 29 19 8 4 1 0

9. Solution
Let a=4 be the assumed mean.
d = x – a = x -4
x f d d2 fd fd2
0 12 -4 16 -48 192
1 17 -3 9 -51 153
2 29 -2 4 -58 116
3 19 -1 1 -19 19
4 8 0 0 0 0
5 4 1 1 4 4
6 1 2 4 2 4
7 0 3 9 0 0
f = 90 fd = -
170
fd2 = 488

10. Solution
N =f = 90
𝑥 = 𝑎 +
 𝑓𝑑
𝑁
= 4 -
170
90
= 2.11
s =
fd2
𝑁
−
fd
𝑁
2
=
488
90
−
−170
90
2
=
1.36

11. Solution
Since the maximum frequency is 29, the mode
is 2.
Sk =
𝑀𝑒𝑎𝑛 −𝑀𝑜𝑑𝑒
s
=
2.11−2
1.36
= 0.08
Hence the graph will asymmetrical.

12. Applications
• Skewness has benefits in many areas.
Many models assume normal distribution;
i.e., data are symmetric about the mean.
• But in reality, data points may not be
perfectly symmetric. So, an understanding
of the skewness of the dataset indicates
whether deviations from the mean are
going to be positive or negative.

13. Application
• Skewness is used in data handling such
as in stock market the with the factors like
skewness, variance , covariance are used
to predict the market.
• So, the skewness can be used in any data
to find how the data is differing from the
mean.