Positively Skewed Distribution

What is Positively Skewed Distribution?

Positively Skewed Distribution is a type of distribution where the mean, median and mode of the distribution are positive rather than negative or zero i.e., data distribution occurs more on the one side of the scale with long tail on the right side. It is also known as the right-skewed distribution, where the mean is generally there to the right side of the median of the data.

Example

Income is said to be positively distributed if more population falls in the normal or lower-income earning group rather than a few high earning income groups. They show the mean is greater than the median.

Below is the data are taken from the sample. In the first column, the Income category is given, and in the second column, the number of persons falling in the respective income group is given. Calculate the meanMeanMean refers to the mathematical average calculated for two or more values. There are primarily two ways: arithmetic mean, where all the numbers are added and divided by their weight, and in geometric mean, we multiply the numbers together, take the Nth root and subtract it with one.read more, medianMedianThe median formula in statistics is used to determine the middle number in a data set that is arranged in ascending order. Median ={(n+1)/2}thread more, and mode of the data sample and analyze whether it is an example of the positively skewed distribution.

Solution:

Calculation of the mean, median and mode:

#1 – Mean:

Mean of the data is:

• Mean = (2,000 + 4,000 + 6,000 + 5,000 + 3,000 + 1,000 + 1,500 + 500 + 100 +150) / 10
• Mean = 2,325

#2 – Median:

• Median Value =(10 + 1 / 2) th value
• Median Value = 5.5 th value i.e. average of 5^th and 6^th value
• Median = (3,000 + 1,000) / 2
• Median = 2,000

#3 – Mode:

The mode will be the highest value in the data set which is 6,000 in the present case.

Analysis:

Here,

• Mean > Median
• 2325 > 2000

In positively distributed data, the mean is greater than the median, and most people fall on the lower side. The same is the case n the above example.

What Causes Positively Skewed Distribution?

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For eg:
Source: Positively Skewed Distribution (wallstreetmojo.com)

#1 – Inequality in Distribution

The amount of money earned by everyone will differ. Earning depends upon the working capacity, opportunities, and other factors. Similarly, the probability of any outcome is different. Hence the main cause of positively skewed distribution in unequal distribution.

#2 – Homogenous Groups

The positive distribution reflects the same line of groups that is there is more or less homogenous kind of the outcomes like in the case of positive income distribution the most population in the lower or middle earning groups, i.e., the earning is more or less homogenous.

#3 – Desirable Returns

In finance, if the returns are desirable, then it is said to be positively distributed. In positive distribution, the chances of profits are more than the loss.

#4 – Predictive Approach

The predictive approach towards the distribution of data into groups also causes such a distribution.

Positively Skewed Distribution Mean and Median

In a Positively skewed distribution, the mean is greater than the median as the data is more towards the lower side and the mean average of all the values, whereas the median is the middle value of the data. So, if the data is more bent towards the lower side, the average will be more than the middle value. Let’s take the following example for better understanding:

• 50, 51, 52, 59 shows the distribution is positively skewed as data is normally or positively scattered range.
• The mean of the data provided is 53 (average, i.e., (50+51+52+59)/4).
• Median is (n+1/2) Value, i.e. (4+1/2), i.e., 2.5, i.e., the median is average of 2^nd value and 3^rd value.
• Median is (51+52)/2 = 51.5
• As the mean is 53 and the median is 51.5, the data is said to be positively skewed.

Central Tendency in Positively Skewed Distribution

Central TendencyCentral TendencyCentral Tendency is a statistical measure that displays the centre point of the entire Data Distribution & you can find it using 3 different measures, i.e., Mean, Median, & Mode.read more is the mean, median, and mode of the distribution. In the normal skewed distribution data, the mean, median, and mode are equal. Whereas the central tendency of positively skewed data has the following equation:

As the mean is average, the median is the middle value, and mode is the highest value in the data distribution. As in this type of data, the results are bent towards the lower side; hence mean will be more than the median as the median is the middle value and mode is always the highest value, and it is always greater than the mean and median in any type of skewed distributionSkewed DistributionSkewness is the deviation or degree of asymmetry shown by a bell curve or the normal distribution within a given data set. If the curve shifts to the right, it is considered positive skewness, while a curve shifted to the left represents negative skewness.read more.

Conclusion

It is the type of distribution where the data is more towards the lower side. That means there are more or less homogenous types of groups. In a positively skewed distribution, most values on the graph shown on the left side of the distribution and the curve are longer towards the right trail. In this distribution, the mean is greater than the median. In finance, It is the chance for more profits than the loss. In the case of the income distribution, if the most population earns in the lower and middle range, then the income is said to be positively distributed. Uneven distribution is the main cause for determining the positive or negative distribution.

Recommended Articles

This has been a guide to what is Positively Skewed Distribution and its definition. Here we discuss an example of positively skewed distribution with their causes and graph. You may also have a look at the following articles –

• Negatively Skewed Distribution
• Central Limit Theorem.
• Standard Error Formula
• Arithmetic Mean
• Geometric Mean