Coefficient of Skewness Calculator

| Added in Statistics

What is the Coefficient of Skewness?

The coefficient of skewness helps you understand the asymmetry of your data distribution. Imagine you're at a carnival game—sometimes the balls cluster to one side or perhaps they're more evenly spread out. This is essentially what skewness measures.

Knowing the skewness of your data can be enormously helpful. It tells you if your data is skewed to the left, skewed to the right, or perfectly symmetrical, which in turn can influence your decisions, whether you're working in finance, healthcare, or quality control.

How to Calculate Coefficient of Skewness

The formula is straightforward:

[\text{Coefficient of Skewness} = \frac{3 \times (\text{Mean} - \text{Median})}{\text{Sample Size}}]

Where:

  • Mean is the average value of your data set.
  • Median is the middle value in your data set.
  • Sample Size is the number of observations in your data set.

To break it down:

  1. Subtract the median from the mean: This gives you the difference between the two central tendency measures.
  2. Multiply the result by 3: Simple scaling.
  3. Divide by the sample size: This normalizes the value, giving you a dimensionless coefficient.

Calculation Example

Imagine you have a sample data set, and you've calculated the following:

  • Mean: 7
  • Median: 5
  • Sample Size: 200

Plugging these values into the formula:

[\text{Coefficient of Skewness} = \frac{3 \times (7 - 5)}{200} = \frac{6}{200} = 0.03]

The coefficient of skewness is 0.03. This low value suggests that your data set is pretty symmetrical.

Summary Table

Statistic Value
Mean 7
Median 5
Sample Size 200
Skewness Coefficient 0.03

Frequently Asked Questions

The coefficient of skewness indicates the asymmetry of your data distribution. A positive value means the data is skewed to the right (tail extends right), a negative value means it is skewed to the left, and a value near zero indicates a symmetrical distribution.

Values between -0.5 and 0.5 indicate fairly symmetrical data. Values between -1 and 1 are considered acceptable for most analyses. Values beyond this range indicate significant skewness that may affect statistical analyses.

The factor of 3 is a scaling constant used in Pearson second skewness coefficient formula. It helps normalize the measure and makes it more sensitive to asymmetry in the distribution.

Skewness analysis is useful when you need to understand data distribution for statistical testing, identify outliers, choose appropriate statistical methods, or when preparing data for machine learning models that assume normal distribution.