Detailed PowerPoint Presentation on Skewness and Kurtosis: A Comprehensive Study of Data Distribution, Statistical Asymmetry, and Tail Behavior with Clear Explanations, Graphical Illustrations, Real-Life Examples, and Applications in Data Analysis, Resear

This presentation explains the fundamental concepts of Skewness and Kurtosis, key measures that describe the shape, symmetry, and tail characteristics of a statistical data distribution. It includes detailed definitions, formulas, types, and visual graphs illustrating positive and negative skewness, and leptokurtic, mesokurtic, and platykurtic curves.

Designed for students and professionals in statistics, data science, and economics, the slides make complex ideas easy to understand through examples, comparisons, and real-world applications. Perfect for academic presentations, research analysis, and classroom learning.

Category: Statistics | Data Analysis | Education

1. SKEWNESS & KURTOSIS

2. Skewness is a statistical measure that
describes the asymmetry of a data
distribution around its average (mean). It
tells us whether the data values are evenly
spread or lean more toward one side of the
distribution curve.
Kurtosis is a statistical measure that
describes the shape of a data distribution’s
tails and how sharply it peaks compared
to a normal (bell-shaped) distribution. It
tells us whether the dataset has more or
fewer extreme values (outliers) than
expected.

3. SKEWNESS SKEWNESS
Skewness is a statistical measure that describes the asymmetry of a probability
distribution. It indicates whether the data points are skewed to the left (negative skew)
or to the right (positive skew) of the mean.

4. TYPESTYPESPositive Skewness (Right Skewness) Negative Skewness (Left Skewness)

5. Positive Skewness (Right Skewness)Positive Skewness (Right Skewness)In a positively skewed distribution, the
right tail (higher values) is longer or
fatter than the left tail (lower values).
The mean is typically greater than the
median, which is greater than the mode .
Example: Income distribution in many
economies, where a small number of
individuals earn significantly higher
incomes than the majority.

6. Negative Skewness (Left Skewness)Negative Skewness (Left Skewness)n a negatively skewed distribution, the
left tail is longer or fatter than the right
tail.
The mean is typically less than the
median, which is less than the mode.
Example: Age at retirement, where most
individuals retire around a certain age,
but a few retire much earlier.

7. CalculationCalculationIt truly scales the value down to a limited range -1 to +1

8. KURTOSIS KURTOSIS
Kurtosis is a statistical measure that describes the shape of a probability distribution's tails
in relation to its overall shape. It provides insight into the extremity of the distribution's
tails and the presence of outliers.
There are several types of kurtosis:
Mesokurtic: This is the kurtosis of a normal distribution, which has a kurtosis value of 3.
It indicates a moderate level of tail thickness.
Leptokurtic: Distributions that have a kurtosis greater than 3 are considered
leptokurtic. These distributions have heavier tails and a sharper peak compared to a
normal distribution, indicating a higher likelihood of extreme values.
Platykurtic: Distributions with a kurtosis less than 3 are termed platykurtic. These
distributions have lighter tails and a flatter peak compared to a normal distribution,
suggesting fewer extreme values

10. LeptokurticLeptokurtic
Higher Peak: The distribution is more concentrated around the mean, resulting in a
sharper peak.
Fatter Tails: The tails of the distribution are heavier, meaning there is a greater
probability of extreme values occurring compared to a normal distribution.
Implications for Data: Leptokurtic distributions are often associated with datasets
that exhibit significant outliers or extreme values. This can be important in fields
such as finance, where extreme market movements are of interest.

11. MesokurticMesokurtic
Kurtosis Value: The kurtosis of a mesokurtic distribution is exactly 3, which means it serves as
a benchmark for comparing other distributions.
Normal Distribution: The normal distribution is the most common example of a mesokurtic
distribution. It has a symmetric bell shape, with data points concentrated around the mean.
Moderate Tail Behavior: Mesokurtic distributions have tails that are neither too heavy (as in
leptokurtic distributions) nor too light (as in platykurtic distributions). This indicates a
balanced probability of extreme values.

12. PlatykurticPlatykurtic
Kurtosis Value: The kurtosis of a platykurtic distribution is less than 3, which signifies
that the distribution has lighter tails and a flatter peak.
Flatter Peak: The distribution is less concentrated around the mean, resulting in a
broader and flatter peak compared to a normal distribution.
Lighter Tails: Platykurtic distributions have tails that are thinner, indicating a lower
probability of extreme values or outliers. This suggests that the data is more evenly
distributed around the mean.

13. PlatykurticPlatykurtic
Kurtosis Value: The kurtosis of a platykurtic distribution is less than 3, which signifies
that the distribution has lighter tails and a flatter peak.
Flatter Peak: The distribution is less concentrated around the mean, resulting in a
broader and flatter peak compared to a normal distribution.
Lighter Tails: Platykurtic distributions have tails that are thinner, indicating a lower
probability of extreme values or outliers. This suggests that the data is more evenly
distributed around the mean.

14. ThankyouThankyou