📐 Measure of Shape

Last Updated: Jan 2026

Measure of Shape describes the shape of data distribution.

It tells us:

• Data kis taraf jhuk raha hai (skewness)
• Data kitna peaked ya flat hai (kurtosis)

🗣 Hinglish Tip: Shape = data ka overall pattern / curve ka nature

Shape helps to:

• Understand data distribution
• Choose correct statistical methods
• Analyze real-world datasets

Types of Measure of Shape

1. Skewness
2. Kurtosis

Skewness

Skewness measures the asymmetry of data distribution.

It shows whether data is:

• Symmetric
• Right-skewed
• Left-skewed

Formula For Population Skewness

$\gamma_1 = \frac{\sum (x_i - \mu)^3}{N\sigma^3}$

Where:

• $\gamma_1$ = population skewness
• $\mu$ = population mean
• $\sigma$ = population standard deviation
• $N$ = population size

Sample Skewness

$g_1 = \frac{\sum (x_i - \bar{x})^3}{(n - 1)s^3}$

🗣 Hinglish Tip: Tail jidhar lambi ho → skewness udhar hoti hai

Types of Skewness

1. Symmetric/Normal Distribution

• Mean = Median = Mode
• Skewness = 0
• Bell shape curve

1. Right-skewed/Positive Skewness

• Mean > Median > Mode
• Skewness > 0

1. Left-skewed/Negative Skewness

• Mean < Median < Mode
• Skewness < 0

Kurtosis

Kurtosis measures the peakedness or flatness of the distribution.

It focuses on:

• Height of the peak
• Weight of the tails

Formula Population Kurtosis

$\beta_2 = \frac{\sum (x_i - \mu)^4}{N\sigma^4}$

Excess Kurtosis

$\text{Excess Kurtosis} = \beta_2 - 3$

(3 is kurtosis of normal distribution)

Types of Kurtosis

🗣 Hinglish Tip: Kurtosis = curve kitni pointed ya flat hai

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