1. Chapter 6: Shape of the Distribution

2. After Completing the chapter ,you will able to :
• Measures the Shape of the distribution
• Computation process of Skewness and Kurtosis
Learning Outcomes

3. From this lecture, you are going to learn…
• Skewness with it's types?
• How to calculate skewness and interpretation.
• Kurtosis with it's types.
• Calculation of kurtosis.
• Class video links
Contents

4. The shape of the data can be understood by considering how the data points are distributed in the space.
This distribution can be categorized into Symmetrical Distribution. Two numerical measures of shape give a
more precise evaluation:
skewness tells you the amount and direction of skew (departure from horizontal symmetry)
kurtosis tells you how tall and sharp the central peak is, relative to a standard bell curve.
Shape of the Distribution

5. Skewness
Skewness: Skewness is the measurement of the lack of symmetry of the distribution. That is
when a distribution is not symmetrical it is called a skewed distribution. In a symmetrical
distribution the value of mean, median and mode are same. In a skewed these values differ.
Skewness tells us about the direction of variation.

6. Skewness

7. Interpretation of Skewness
The range of the coefficient of skewness (SKp ) is lies between -3 to +3.
•If SKp=0; symmetric Distribution.
•If SKp >(0 upto 1);Skewed Distribution
• If SKp >(1 upto 2);Moderately Skewed Distribution
•If SKp >(2 upto 3);Highly Skewed Distribution
*Same Comment Applicable for negative value.
Suppose If SKp = -1.75; the distribution is moderately skewed which is
negative.

8. Example

9. Kurtosis
Kurtosis: Kurtosis refers the degree of flatness or peakness in
the region about the mode of a frequency curve. That is,
their peakness or flatness.
Three types of distributions with respect to kurtosis:
1. Leptokurtic distribution: Peaked distribution or more
peaked then symmetric curve.
2. Platykurtic distribution: Flat distribution or less peaked
then symmetric curve
3. Mesokurtic distribution: Normal distribution or
symmetrical distribution.

10. Kurtosis

11. Exercise..
•Marks of 10 students in a class.
15, 25, 48, 50,65,95,18,85,75,55. Calculate coefficient of skewness and interpret the
result.
•Time of reading newspaper of 6 people(in hour)
3,4,2,4,6,2,5.
Calculate coefficient of kurtosis.

12. https://www.youtube.com/watch?v=zwPEXv_eoxE&t=509s
https://www.youtube.com/watch?v=BGkJmmRBntI
Class Video Links