1. What is Skewness?

Skewness is a measure of the asymmetry of the probability distribution of a real-valued random variable about its mean. It describes the extent to which a distribution differs from a normal distribution, either to the left or right.

2. How Does the Calculator Work?

The calculator uses the skewness formula:

Where:

• Mean — The average value of the dataset
• Median — The middle value of the dataset
• Standard Deviation — A measure of data dispersion

Interpretation: A skewness value of 0 indicates a symmetrical distribution. Positive values indicate right-skewed distributions, while negative values indicate left-skewed distributions.

3. Importance of Skewness Calculation

Details: Skewness is important in statistics as it helps identify the shape of data distribution. Many statistical tests and models assume normally distributed data, so measuring skewness helps determine if data transformation is needed before analysis.

4. Using the Calculator

Tips: Enter the mean, median, and standard deviation values. All values should be unitless as skewness is a dimensionless quantity. Standard deviation must be greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What does a positive skewness value indicate?
A: Positive skewness indicates that the distribution has a long right tail, with most data points concentrated on the left side of the distribution.

Q2: What does a negative skewness value indicate?
A: Negative skewness indicates that the distribution has a long left tail, with most data points concentrated on the right side of the distribution.

Q3: What is considered a significant skewness value?
A: Generally, skewness values between -0.5 and 0.5 indicate approximately symmetric distributions. Values between -1 and -0.5 or 0.5 and 1 indicate moderate skewness, and values beyond -1 or 1 indicate highly skewed distributions.

Q4: Are there other methods to calculate skewness?
A: Yes, there are several formulas for skewness, including Pearson's first and second coefficients of skewness, and the Fisher-Pearson standardized moment coefficient.

Q5: When is this formula most appropriate?
A: This formula works best for unimodal distributions that are not extremely skewed. For more precise measurements, especially with small samples, other formulas might be more appropriate.