3.12:

3.12: Skewness

JoVE Core
Statistics

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JoVE Core Statistics

Skewness

3.13: Types of Skewness

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01:06 min

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April 30, 2023

Overview

The measures of central tendency calculated from a data set may not reveal much about its intrinsic distribution. If a plot is made of the data set’s values, the mean and the median may not only differ, but also the plot may have more values on one side of the central tendencies. Such a data set is said to be skewed towards that side.

The longer the tail of the plot on one side, the more skewed it is. The skewness of a data set’s values suggests that the measures of central tendency are somewhat crude, missing out on the finer details. In a symmetrical distribution, the mean, median, and mode are the same, while in an asymmetric distribution or skewed data set, the mean and median lie to the left or right of the mode.

For example, the mean income distribution of a country does not shed much light on its income inequality. While a few wealthiest individuals may earn a lot, the majority of the population may earn abysmally. Therefore, income distribution represents a skewed data set.

Transcript

Comparison between mean, median, and mode provides information on how data is distributed.

In this example graph, the left side of the graph is the mirror image of the right side. It is called the symmetrical or normal distribution of the data.

In such normally distributed graph, the mean, median, and mode values lie in the same position indicated by the dotted line.

Suppose the left and right side of the graph is not the same; it results in the skewness in the distribution. Here, the mean, median, and mode are not the same and reflect the different values in the data set.

Skewness indicates the presence of outliers. For instance, in this case, the outliers are present on the right side of the graph.

Skewness is often used to make investment decisions. The skewness in the returns of an investment model indicates whether the investment will give frequent smaller gains and few huge losses; or frequent losses and a few large wins.

Key Terms and definitions

Skewness in Statistics - Refers to a data set's asymmetry around its mean.
Mean - Represents the average value from a data set.
Median - The middle value in an ordered data set.
Skewed Distribution - Data set where values cluster more on one side of the scale.
Income Distribution Skewness - Describes income inequality in a population.

Learning Objectives

Define Skewness – Understand its relationship with data set distribution (e.g., skewness in statistics).
Contrast Mean and Median – Understand how they can differ in skewed data sets (e.g., skewness mean median).
Explore Distribution Examples – Look at income inequality as an example (e.g., income distribution skewness).
Explain Skewed Distribution – Understand how data concentrates more on one side of the scale.
Apply in Data Analysis Context – Understand how skewness interpretation can influence data analysis.

Questions that this video will help you answer

What is skewness in statistics and how does it relate to mean and median?
What can a skewed distribution reveal in a dataset?
In what way does income distribution skewness demonstrate the concept?

This video is also useful for

Data Analysts – Understand how skewness interpretation supports data analysis.
Educators – Provides a framework to teach statistical distribution and central tendency.
Economists – Relevant for interpreting socioeconomic data like income distribution.
Statistics Students – Offers insights into concepts like skewness, mean, and median.

Tags

Skewness Central Tendency Data Distribution Mean Median Mode Asymmetric Distribution Symmetrical Distribution Income Inequality Data Set Analysis Income Distribution Skewed Data