Skewness Meaning Types And Examples

Skewness Meaning

Types of Skewness

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

So basically, there are two types:

Positive: The distribution is positively skewedDistribution Is Positively SkewedA positively skewed distribution is one in which the mean, median, and mode are all positive rather than negative or zero. The data distribution is more concentrated on one side of the scale, with a long tail on the right.read more when most of the distribution frequency lies on the right side and has a longer and fatter right tail where the distribution’s Mean > median > Mode.
Negative: The distribution is negatively skewed when most of the distribution frequency lies on the left side and has a longer and fatter left tail. Where the distribution’s Mean < Median < Mode.

Formula

The 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 below –

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

Pearson’s first coefficients (mode Skewness): It is on 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, mode, and standard deviation.

Formula: (Mean – Mode)/Standard Deviation.

Pearson’s second coefficient (median skewness): It is on the distribution’s mean, median, and standard deviation.

Formula: (Mean – Median)/Standard Deviation.

As you can see above, Pearson’s first coefficient of skewness has a mode as its one variable to calculate it. It is useful when data has a more repetitive number in the data set. However, suppose only a few repetitive data in the data set belong to mode. In that case, 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 the median of the data set instead of the 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 one can use it to make for data set(b) as it has a more repetitive mode.

Another way to calculate skewness is by using the below formula:

= Random variable.X = Distribution Mean.N = Total variable in the distribution.α = Standard Deviation.

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Example of Skewness

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

Solution

Use the below data:

Calculation of Distribution Mean

= ($40012+$5008+$7005+$8503+$1000*2)/30Distribution Mean = 561.67

Calculation of Standard Deviation

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

Calculation of Skewness can be done as follows –

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 the distribution data skew from the normal distribution.

Advantages

Skewness is better for measuring the performance of investment returns.The investor uses it when analyzing the data set as it considers the extreme of the distribution.It is a widely used tool in statistics as it helps understand how much data is asymmetry from the normal distribution.

Disadvantages

Skewness ranges from negative to positive infinity. Sometimes, it is 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 data distribution skews, this model will not reflect the actual result in its assumption.

Importance

Statistics play an important role when the data distribution is not normal. The extreme data points in the data set can lead data distribution to skew towards the left (extreme data in the data set are smaller, which skew the 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 with a short-term holding period to analyze the data to identify the trend falling at the end of the distribution.

Conclusion

Skewness is how much the data set deviates from its normal distribution. A larger negative value in the data set means the distribution is negatively skewed, and a larger positive value in the data set means the distribution is positive. It is a good statistical measure that helps the investor predict distribution returns.