Coefficient of Skewness Calculator

Coefficient of Skewness Calculator









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Disclaimer: All calculators in the Textile Calculator have been reviewed by the relevant textile industry experts.

Formula for Coefficient of Skewness

Karl Pearson’s Coefficient of Skewness Formula:

Skewness (Sk)=3(Xˉ−Median)σ\text{Skewness (Sk)} = \frac{3(\bar{X} - \text{Median})}{\sigma}Skewness (Sk)=σ3(Xˉ−Median)​

Where:

  • Xˉ\bar{X}Xˉ = Mean
  • Median = Median of the dataset
  • σ\sigmaσ = Standard Deviation

What Is Coefficient of Skewness?

The coefficient of skewness measures how data spreads across the average value. It checks if the data shifts to one side. In textile manufacturing, we apply this in quality testing, yarn strength data, color fastness scores, or customer satisfaction rates.

You calculate it using this formula:

Skewness (Sk)=3(Xˉ−Median)σ\text{Skewness (Sk)} = \frac{3(\bar{X} - \text{Median})}{\sigma}Skewness (Sk)=σ3(Xˉ−Median)​

Here:

  • Mean (𝑋̄) is the average
  • Median is the middle value
  • Standard Deviation (σ) is the spread of values

Why Skewness Matters in Textile Manufacturing

Skewness shows how consistent our results are. In the dyeing section, if most samples are lighter or darker than the standard, it means the data is skewed. A positive skew means most values are below average. A negative skew means most values are above average.

Skewness in Textile Manufacturing
Skewness in Textile Manufacturing

In textile labs, I often test yarn tenacity. If the skewness is too high or too low, it signals that something went wrong in production. It helps me adjust machines or raw material input.

How the Calculator Works

The coefficient of skewness calculator takes three values: mean, median, and standard deviation. Then it shows if the data is:

  • Symmetrical (Sk = 0)
  • Positively skewed (Sk > 0)
  • Negatively skewed (Sk < 0)

You just enter values, click calculate, and the result appears. It saves time and avoids errors from manual calculation.

Real-Life Use in Textile Production

Let me share a short example from my own work. I checked the GSM values of knitted fabric rolls. The standard GSM was 160, but some rolls showed 145, 150, 170, and 180. I calculated the mean and median, then used the calculator.

I got a positive skew. It showed that more rolls were underweight. I checked the knitting settings and fixed the feeder tension. The next batch had balanced GSM.

This is how the coefficient of skewness helps maintain quality.

Benefits for Fashion Designers and Textile Engineers

Helps in Quality Analysis

I use it to check if the data follows a normal curve. If not, I dig into the process.

Fast Results for Production Lines

You do not need to stop the line to check data. The calculator gives the answer instantly.

Easy to Use

It works with simple input. No need for Excel or complex statistics.

How to Use the Calculator

Step-by-Step Guide

  1. Enter your mean value
  2. Enter the median
  3. Enter the standard deviation
  4. Click “Calculate”
  5. Check the result below

You can use the “Refresh” button to start again.

Common Applications in Textile Industry

In all of these, skewness shows how far the values spread from the center.

Skewness in Trend Forecasting

Fashion designers track reviews and sales data. If most feedback scores fall on one side, it helps plan the next collection. Skewness in customer scores can tell what design or fabric was too trendy or too plain.

Skewness and Product Consistency

Skewness helps us maintain product consistency. When we get a symmetrical value (Sk = 0), it means most products are similar. This is what buyers want—stable quality.

Final Words

The coefficient of skewness calculator helps me improve textile quality. It is simple, fast, and useful. I suggest all textile engineers and fashion designers use it in data checks. Whether in the lab or the factory, skewness tells us more about data shape than just the average.

Try it and check your next report with better insight.