What does Theil index 0 mean?

A Theil index of 0 indicates perfect equality. There is no upper bound for the Theil T index; for Theil L (also called mean log deviation), the maximum value is ln(n) where n is the population size.

Why use Theil over Gini?

Theil indices are additively decomposable — total inequality can be separated into within-group and between-group components — which Gini cannot do. This makes Theil ideal for analysing inequality sources across regions or demographic groups.

Theil Index Income Inequality

Compute the Theil T and Theil L indices for income inequality, which allow decomposition into within-group and between-group inequality components. Theil T = (1/n)∑(yᵢ/μ)ln(yᵢ/μ).

Data set — comma or newline separated

Statistical Results — n = 8

Count (n)8

Sum (Σx)40

Min2

Max9

Range7

Q14

Q35.5

IQR1.5

Mean (μ)5

Median4.5

Mode4

Pop. Variance (σ²)4

Pop. Std Dev (σ)2

Sample Variance (s²)4.571428571

Sample Std Dev (s)2.138089935

Skewness0.65625

Excess Kurtosis-0.21875

How to Use

Enter the values for the scenario you are assessing. Compute the Theil T and Theil L indices for income inequality, which allow decomposition into within-group and between-group inequality components. Theil T = (1/n)∑(yᵢ/μ)ln(yᵢ/μ). Use the theil index result to inform your calculation.

Theil Index Income Inequality

How to Use

Frequently Asked Questions

What does Theil index 0 mean?

Why use Theil over Gini?