About Skewness Formula
The skewness formula is used to measure the asymmetry of distribution when the graph is shown in a skewed manner. Skewness exposes a probability distribution's asymmetry. Skewness is a statistical measure used to indicate a probability distribution's asymmetry.
What do you mean by Skewness Formula?
Skewness can be either positive or bad, regardless of symptoms. We must first determine the mean and variance of the given data before learning how to calculate the skewness using the skewness. It could be both positive and negative. The skewness formula is as follows:
Here, x? is the sample mean, xi is the ith sample, while n is the total number of observations, s is the standard deviation and g is sample skewness
Solved Example of Skewness Formula
Example: 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 |
Sol: We'll calculate skewness to see how skewed these data are in comparison to others.
It is necessary to determine the sample size and sample mean. N = 5 + 18 + 42 + 27 + 8 = 100
x? = {(61 x 5)+(64 x 18)+(67 x 42)+(70 x 27)+(73 x 8)}/ 100
x? =6745/100 = 67.45
The skewness formula can now be used to get the mean.
| Class Marks(x) | Frequency | xf | (x - x?) | (x - x?)2 |
| 61 | 5 | 305 | -6.45 | 208.01 |
| 64 | 18 | 1152 | -3.45 | 214.25 |
| 67 | 42 | 2814 | -0.45 | 8.51 |
| 70 | 27 | 1890 | 2.55 | 175.57 |
| 73 | 8 | 584 | 5.55 | 246.42 |
| =6745 | =852.75 | |||
| =67.45 | =8.5275 |
Now, determining skewness:
s=√[(8.5275/(100−1))=0.2935]
g=√[(−2.693/[99∗(0.295)3]=−1.038
The following are Bulmer's skewness interpretation rules
- The data distribution is severely skewed if the skewness is less than -1 or larger than +1.
- The data distribution is said to be considerably skewed if the skewness is between -1 and -1/2 or between +1/2 and +1.
- When the skewness is between 1/2 and +1/2, the data is essentially symmetrically distributed.
Answer: Skewness is -1.038
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