This document provides information about skewness and kurtosis. It defines skewness as a measure of the asymmetry of a probability distribution about its mean, indicating the direction and amount of skew. Kurtosis is defined as a statistical measure that identifies how heavily the tails of a distribution differ from a normal distribution. The document discusses positive and negative skewness, as well as leptokurtic, mesokurtic, and platykurtic kurtosis. It provides examples of symmetrical, positively skewed, and negatively skewed distributions and explains how to calculate and compare skewness and kurtosis values.

1. SKEWNESS
AND KURTOSIS

2. HELLO!
I am Abdulla Al Moin
Department of Computer Science Engineering
find me at abdulla15-2838@diu.edu.bd
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3. Submitted To
Atia Sanjida Talukder
Lecturer
Dept. of GED
Daffodil International University
Email: atiasanjida.ged@diu.edu.bd
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4. SKEWNESS
Let’s start with the first set of slides 1 4

5. Skewness is a measure of asymmetry of the probability distribution of a random
variable about its mean. In other words, skewness tells us the amount and direction of
skew (departure from horizontal symmetry).
The skewness value can be positive or negative, or even undefined.
Defining SKEWNESS
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6. SKEWS
If skewness is 0, the data are perfectly symmetrical, although it is
quite unlikely for real-world data. As a general rule of thumb:
◉ If skewness is less than -1 or greater than 1, the distribution is
highly skewed.
◉ If skewness is between -1 and -0.5 or between 0.5 and 1, the
distribution is moderately skewed.
◉ If skewness is between -0.5 and 0.5, the distribution is
approximately symmetric.
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7. Calculating SKEWNESS
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8. Besides positive and negative skew, distributions can also be said to have zero or
undefined skew.
There are several ways to measure skewness. Pearson’s first and second coefficients of
skewness are two common ones.
Explaining Skewness
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9. Symmetrical Distribution:
Positively Skewed Distribution:
Negatively skewed distribution:
DISTRIBUTION-RELATIONSHIP OF MEAN AND MEDIAN
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10. ◉ Karl-Person coefficient of skewness
◉ Bowley’s coefficient of skewness
◉ Coefficient of skewness based on
moments
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SOME IMPORTANT MEASURES OF SKEWNESS

11. Kurtosis is a statistical measure that defines how heavily the tails of a distribution differ
from the tails of a normal distribution.
In other words, kurtosis identifies whether the tails of a given distribution contain
extreme values.
Defining KURTOSIS
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12. ◉ Mesokurtic
◉ Leptokurtic
◉ Platykurtic
Types of KURTOSIS
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13. Calculating KURTOSIS
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14. AND TABLES TO COMPARE DATA
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Kurtosis for 7 Simple Distributions Also Differing in Variance
X freq A freq B freq C freq D freq E freq F freq G
05 20 20 20 10 05 03 01
10 00 10 20 20 20 20 20
15 20 20 20 10 05 03 01
Kurtosis -2.0 -1.75 -1.5 -1.0 0.0 1.33 8.0
Variance 25 20 16.6 12.5 8.3 5.77 2.27
Shoulder
s
5,
15
5.5,
14.5
5.9.
14.1
6.5,
13.5
7.1,
12.9
7.6,
12.4
8.5,
11.5
Platykurtic Leptokurtic

15. “
Skewness and kurtosis are a
fundamental statistics concept that
everyone in statistics and analytics
needs to know. It is something that we
simply can’t run away from. .
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16. THANKS!
Any questions?
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