Skewness Formula
When the graph plotted is displayed in a skewed manner, the skewness formula is used to measure the asymmetry of a distribution. Skewness reveals the asymmetry of a probability distribution. Skewness is a statistical measure to help reveal the asymmetry of a probability distribution. Let us learn more about the skewness formula in more detail.
What is Skewness Formula?
Skewness measured can either be positive or negative, irrespective of signs. Before we learn about calculating the skewness using the skewness, we have to first find the mean and variance of the given data. It can be positive or negative. The skewness formula is:
\(g=\frac{\sum_{i=1}^{n}\left(x_{i}\bar{x}\right)^{3}}{(n1) s^{3}}\)
Where,
 \(\bar{x}\) is the sample mean
 \(x_{i}\) is the i^{th} sample, while n is the total number of observations
 s is the standard deviation
 g sample skewness
Let us learn a solved example to apply the skewness formula.
Solved Examples Using Skewness Formula

Example 1: Using the skewness formula, find the skewness for the following data.
Weight (Kg) Class Marks Frequency 59.5 – 62.5 61 5 62.5 – 65.5 64 18 65.5 – 68.5 67 42 68.5 – 71.5 70 27 71.5 – 74.5 73 8 Solution:
We will compute the skewness to know how skewed these data are as compared to other data sets.
The sample size and sample mean should be found out.
N = 5 + 18 + 42 + 27 + 8 = 100
\[\begin{array}{l}
\bar{x}=\frac{(61 \times 5)+(64 \times 18)+(67 \times 42)+(70 \times 27)+(73 \times 8)}{100} \\
\bar{x}=\frac{6745}{100}=67.45
\end{array}\]
Now the mean can be computed using the skewness formula.
\[\begin{array}{llllll}
\hline \text { Class Mark, } x & \text { Frequency, } f & x f & (x\bar{x}) & (x\bar{x})^{2} \times f & (x\bar{x})^{3} \times f \\
\hline 61 & 5 & 305 & 6.45 & 208.01 & 1341.68 \\
\hline 64 & 18 & 1152 & 3.45 & 214.25 & 739.15 \\
\hline 67 & 42 & 2814 & 0.45 & 8.51 & 3.83 \\
\hline 70 & 27 & 1890 & 2.55 & 175.57 & 447.70 \\
\hline 73 & 8 & 584 & 5.55 & 246.42 & 1367.63 \\
\hline & & 6745 & \text {n/a}&852.75 & 269.33 \\
\hline && 67.45 & \text {n/a}& 8.5275 & 2.6933 \\
\hline
\end{array}\]
Now, determining the skewness:
\(g=\frac{\sum_{i=1}^{n}\left(x_{i}\bar{x}\right)^{3}}{(n1) s^{3}}\)
\(s=\sqrt{[}(8.5275 /(1001))=0.2935]\)
\(g=\sqrt{[}\left(2.693 /\left[99 *(0.295)^{3}\right]=1.038\right.\)
Bulmer rules for interpreting the skewness are:
 If the skewness is less than 1 or greater than +1, then the data distribution is highly skewed
 If the skewness is between 1 and \(\frac{1}{2}\) or between \(+\frac{1}{2}\) and +1, then the data distribution can be said to be moderately skewed.
If the skewness is between \(\frac{1}{2}\) and \(+\frac{1}{2}\), the data is distributed almost symmetrically.
Answer: Skewness is 1.038
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