Skewness

Skewness Meaning

Skewness describes how much statistical data distribution is asymmetrical from the normal distribution, where distribution is equally divided on each side. If a distribution is not symmetrical or Normal, then it is skewed, i.e., it is either the frequency distribution skewed to the left side or to the right side.

Types of Skewness

If the distribution is symmetric, then it has a skewness of 0 & its Mean = Median = Mode.

So basically, there are two types –

  • Positive: The distribution is positively skewed when most of the frequency of distribution lies on the right side of distribution & has a longer and fatter right tail. Where the distribution’s Mean > median > Mode.
  • Negative: The distribution is negatively skewed when most of the frequency of distribution lies on the left side of distribution & has a longer and fatter left tail. Where the distribution’s Mean < Median < Mode.

Formula

Skewness formulaSkewness FormulaSkewness Formula helps in determining the probability distribution of the given set of variables. Based on a statistical formula, the skewness can be positive, negative or undefined. Skewness = ∑Ni (Xi – X)3 / (N-1) * σ3 read more is represented as below –

Skewness Formula

There are several ways to calculate the skewness of the data distribution. One of which is Pearson’s first & second coefficients.

  • Pearson’s first coefficients (Mode Skewness): It is based on the Mean, Mode & Standard deviation of the distribution.

Formula: (Mean – Mode)/Standard Deviation.

  • Pearson’s second coefficients (Median Skewness): It is based on the Mean, Median & Standard deviation of the distribution.

 Formula: (Mean – Median)/Standard Deviation.

As you can see above that Pearson’s first coefficient of skewness has a mode as its one variable to calculate it & it is useful only when data has a more repetitive number in the data set, Like if there are only a few Repetitive data in the data set which belong to mode, then Pearson’s second coefficient of skewness is a more reliable measure of 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 as it considers median of the data set instead of mode.

For Example:

Data set (a):  7,8,9,4,5,6,1,2,2,3.

Data set (b):  7,8,4,5,6,1,2,2,2,2,2,2,2,2,2,2,3.

For both the data sets, we can conclude the mode is 2. But it does not make sense to use Pearson’s first coefficient of skewness for data set(a) as its number 2 appears only twice in the data set, but it can be used to make for data set(b) as it has a more repetitive mode.

Another way to calculate skewness by using the below formula:

Skewness Formula
  • = Random variable.
  • X = Distribution Mean.
  • N = Total variable into the distribution.
  • α = Standard Deviation.
Skewness

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For eg:
Source: Skewness (wallstreetmojo.com)

Example of Skewness

To understand this concept in more detail, let’s look into the below example:

You can download this Skewness Excel Template here – Skewness Excel Template
In XYZ management college, 30 final year student is considering job placement into the QPR research firm & their compensations are based on student’s academic performance & past work experience. Below are the data of the student’s compensation in the PQR research firm.

Solution

Use the below data

Example 1

Calculation of Distribution Mean 

Skewness Example 1.1
  • = ($400*12+$500*8+$700*5+$850*3+$1000*2)/30
  • Distribution Mean = 561.67

Calculation of Standard Deviation

Example 1.2
  • Standard Deviation= √{(Sum of the deviation square * No. of students)/N}.
  • Standard Deviation = 189.16

Calculation of Skewness can be done as follows –

Example 1.3
  • Skewness: (sum of the Deviation Cube)/(N-1) * Standard deviation’s Cube.
  • = (106374650.07) / (29 * 6768161.24)
  • = 0.54

Hence, the value of 0.54 tells us that distribution data is slightly skewed from the normal distribution.

Advantages

  • Skewness is better to measure the performance of the investment returns.
  • The investor uses this when analyzing the data set as it considers the extreme of the distribution rather than relying only on the
  • It is a widely used tool in the statistics as it helps understanding how much data is asymmetry from the normal distribution.

Disadvantages

  • Skewness range from negative infinity to positive infinity & it sometimes becomes difficult for an investor to predict the trend in the data set.
  • An analyst is forecasting the future performance of an asset using the financial model, which usually assumes that data is normally distributed, but if the distribution of data is skewed, then this model will not reflect the actual result in its assumption.

Importance

In statistics, it plays an important role when distribution data is not normally distributed. The extreme data points into the data set can lead data distribution to skew towards left (i.e., extreme data into the data set are smaller, that skew data set negative which results mean<median<mode ) or to skew towards the right (i.e., extreme data are larger, that skew data set positive which results mean>median>mode). It helps an investor who has a short term holding period to analyze the data to identify the trend,  which is falling on the extreme end on the distribution.

Conclusion

Skewness is simply how much data set is deviating from its normal distribution. A larger negative value in the data set means that distribution is negatively skewed & larger positive value in the data set means that distribution is positively distributed. It is a good statistical measure that helps the investor to predict returns from the distribution.

Recommended Articles

This has been a guide to Skewness and its meaning. Here we discuss how to calculate skewness along with its calculation and an example. Here we also discuss its advantages, disadvantages, and importance. You may also have a look at the following articles –

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