The skewed distribution is a type of distribution whose mean value does not directly coincide with its peak value. Skewness is the measure of the asymmetricity of a distribution. Symmetric distribution is the one whose two halves are mirror images of each other. On the other hand, asymmetric or skewed distribution has one of the tails longer than the other. Most of the data recorded in real life follow an asymmetric or skewed distribution.

**Types of Skewed Distribution**

### 1. Positively Skewed Distribution

If a distribution has a tail on the right side, it is said to be positively skewed or right-skewed distribution. More values are plotted on the left side of the distribution, and only a few of them are present on the right or the tail side. The mean of the distribution has a positive value and is present on the right side of the median and mode of the data.

### 2. Negatively Skewed Distribution

If a distribution has a tail on the left side, it is said to be negatively skewed or left-skewed distribution. More values are plotted on the right side of the distribution, and only a few of them are present on the left or the tail side. The mean of the distribution can be zero or negative and has less magnitude as compared to the median and mode.

**Examples of Skewed Distribution**

### 1. Cricket Score

Cricket score is one of the best examples of skewed distribution. Let us say that during a match, most of the players of a particular team scored runs above 50, and only a few of them scored below 10. In such a case, the data is generally represented with the help of a negatively skewed distribution. Similarly, a positively skewed distribution can be used if most of the players of a particular team score badly during a match, and only a few of them tend to perform well.

### 2. Exam Results

The representation of exam results forms a classic example of skewed distribution in real life. The distribution of scores obtained by the students of a class on any particularly difficult exam is generally positively skewed in nature. This is because due to the increased difficulty level of the exam, a majority of students tend to score low, and only a few of them manage to score high. Similarly, the distribution of scores obtained on an easy test is negatively skewed in nature because the reduced difficulty level of the exam helps more students score high, and only a few of them tend to score low.

### 3. Average Income Distribution

Income distribution is a prominent example of positively skewed distribution. This is because a large percentage of the total people residing in a particular state tends to fall under the category of a low-income earning group, while only a few people fall under the high-income earning group. The mean of such data is generally greater than the other measures of central tendency of data such as median or mode.

### 4. Human Life Cycle

The human life cycle is a classic example of asymmetrically distributed data. This is because most people tend to die after reaching an average age, while only a few people die too soon or too late. If such data is plotted along a linear line, most of the values would be present on the right side, and only a few values would be present on the left side. Hence, the representation is clearly left or negatively skewed in nature.

### 5. Taxation Regimes

Due to the unequal distribution of wealth and income, the taxation regimes vary from country to country. Most of the people pay a low-income tax, while a few of them are required to pay a high amount of income tax. The distribution is clearly asymmetric in nature, hence such data can be represented easily with the help of a right or positively skewed distribution.

### 6. Real Estate Prices

Real estate prices can be represented easily with the help of skewed distribution. Usually, most of the houses, plots, buildings, etc., have a lower value, while only a few of them are incredibly expensive. This means if the prices of all the real estate options available in a locality are plotted along a linear line, more values will be plotted on the left side, and only a few values will be plotted on the right side, thereby forming a tail on the right side. Hence, it forms a prominent example of a right or positively skewed distribution.

### 7. Retirement Age

Most people tend to choose retirement around the age of 50, while a few of them opt to retire in their 40s. If such data is required to be represented graphically, the most suited distribution would be left or negatively skewed distribution.

### 8. Movie Ticket Sales

The pictorial representation of the movie ticket sales per month is yet another example of skewed distribution in real life. For instance, if most of the movies released during a month are boring or inappropriate to the customers, and only a few of them are blockbusters, then the movie ticket sales of that particular month can be represented with the help of positively skewed distribution.

### 9. Record of Long Jumps at a Competition

If you record the length of the jumps of the long jumpers participating in the Olympics or at any other athletic competition, you can easily observe that most of the jumpers tend to land a jump to a larger distance, while only a few of them land their jump to shorter lengths. This clearly demonstrates a negatively or left-skewed distribution because more values are plotted on the right side, and only a few are plotted on the left side; therefore, the tail is formed on the left side.

### 10. Distribution of Stock Market Returns

The representation of stock market returns is usually done with the help of negatively skewed distribution. This is because the stock market mostly provides slightly positive returns on most days, and the negative returns are only observed occasionally. Hence, the graphical representation of data definitely has more points on the right side as compared to the left side.

Thanks for your examples given for skewed densities and frequencies – I am busy with them!

find me at researchgate.

Marcus Hellwig