Skewness – Concept, Types & Importance 📈📘

In statistics, Skewness measures the degree of asymmetry in a frequency distribution. A perfectly symmetric distribution (like the normal distribution) has zero skewness.

But in real-life data — income, sales, prices, marks — distributions are often skewed.

Understanding skewness helps interpret whether data are pulled toward higher values or lower values.

1. Meaning of Skewness

A distribution is skewed if it is not symmetrical about the mean.

• If the right tail is longer, the distribution is positively skewed.
• If the left tail is longer, the distribution is negatively skewed.

2. Symmetrical Distribution

A distribution is symmetrical when:

• Mean = Median = Mode
• Both halves mirror each other

Characteristics

• No skewness
• Balanced data
• Bell-shaped appearance

3. Types of Skewness

1) Positive Skewness (Right-Skewed)

• Tail extends to the right
• More values are on the lower side

Relation between Averages

Mean > Median > Mode

Real-life Examples

• Income distribution
• Housing prices
• Insurance claims

2) Negative Skewness (Left-Skewed)

• Tail extends to the left
• More values are on the higher side

Relation between Averages

Mean < Median < Mode

Examples

• Retirement ages
• Scores where most students score high

3) Zero Skewness (Symmetrical)

• Tail lengths equal
• Mean = Median = Mode
• Rare in real-life but common in theoretical models

4. Graphical View (Conceptual)

Symmetrical:        Positive Skew:        Negative Skew:
   (Normal)          (Tail Right)          (Tail Left)

      /\                  /\                    /\
     /  \                /  \                  /  \
    /    \              /    \__            __/    \
   /      \            /        \          /        \

(These shapes help students visualize the direction of tail stretching.)

5. Measures of Skewness (Overview)

Skewness can be measured using:

• Karl Pearson’s Coefficient of Skewness
• Bowley’s Coefficient of Skewness
• Kelly’s Coefficient

(Detailed formulas will be covered in upcoming chapters.)

6. Importance of Skewness

Understanding skewness helps in:

• Business forecasting
• Investment and risk analysis
• Pricing decisions
• Quality control
• Market research
• Understanding concentration of values

7. Solved Example

Consider the following distribution:

Mean = 60
Median = 55
Mode = 50

Interpretation

Since:

Mean > Median > Mode

This distribution is positively skewed.

Another example:

Mean = 40
Median = 44
Mode = 48

Interpretation:

Mean < Median < Mode

The distribution is negatively skewed.

8. Summary ✨

• Skewness = lack of symmetry
• Types: Positive, Negative, Zero
• Right tail → Positive skew
• Left tail → Negative skew
• Mean–Median–Mode relationship helps identify skewness
• Helps in understanding data behaviour

Quiz Time 🎯