Skewness is a measure that quantifies the degree of asymmetry of a distribution around its mean. Positive skewness indicates a distribution with an asymmetric tail extending towards more positive values, while negative skewness indicates a distribution that tails towards more negative values. The Skewness Coefficient Calculator provides a numeric value representing this asymmetry, aiding analysts and researchers in interpreting data more effectively.
Formula of Skewness Coefficient Calculator
The formula to calculate skewness is
Here:
- n represents the number of observations in your dataset.
- x_i is each individual data point.
- x̄ is the average or mean of the dataset.
- s is the standard deviation, which measures the dispersion of a dataset relative to its mean.
Application Table
To aid in practical applications, here is a table with common skewness values:
| Skewness Value | Interpretation |
|---|---|
| Near 0 | Fairly symmetrical distribution |
| Greater than 0 | Data is skewed to the right |
| Less than 0 | Data is skewed to the left |
This table helps users understand common results without needing to perform calculations manually each time.
Example of Skewness Coefficient Calculator
Consider a dataset with the following values: 3, 4, 5, 6, 7, 18. Let’s calculate the skewness.
- Mean (x̄): 7.17
- Standard Deviation (s): 5.77
- Calculation using the skewness formula provides a skewness coefficient, indicating significant positive skew due to the value 18.
Most Common FAQs
A: Skewness is a statistical measure that tells us how asymmetrical a distribution is around its mean.
A: It quantifies the direction and degree of skew, helping predict and interpret dataset behaviors.
A: A positive skew indicates that most values are concentrated on the left with some outliers on the right. A negative skew indicates a concentration on the right.