The graphical method of studying dispersion is known as the Lorenz curve method. This method is used to analyze the distribution of a variable within a population or sample. It provides a visual representation of how the variable is spread across different segments or groups.

Understanding the Lorenz curve method:

The Lorenz curve method is based on the Lorenz curve, which is a graph that compares the cumulative percentage of a variable with the cumulative percentage of the population or sample. It was developed by Max O. Lorenz in 1905 and is commonly used to study income inequality.

Steps in constructing a Lorenz curve:

1. Arrange the variable in ascending order: First, arrange the variable in ascending order, from the smallest value to the largest.

2. Calculate cumulative percentages: Calculate the cumulative percentage of the variable by dividing the cumulative sum of the variable by the total sum of the variable. This gives the proportion of the variable accounted for by each segment.

3. Calculate cumulative population percentages: Calculate the cumulative percentage of the population by dividing the cumulative sum of the population by the total population. This gives the proportion of the population accounted for by each segment.

4. Plot the Lorenz curve: Plot the cumulative percentage of the variable on the y-axis and the cumulative percentage of the population on the x-axis. Connect the points to form a curve.

Interpreting the Lorenz curve:

The Lorenz curve provides insights into the distribution of the variable under study. It helps us understand the concentration or dispersion of the variable across different segments of the population or sample. The closer the Lorenz curve is to the line of perfect equality (a 45-degree line), the more evenly the variable is distributed. On the other hand, if the Lorenz curve deviates from the line of perfect equality, it indicates inequality or concentration of the variable.

The Lorenz curve method allows researchers to compare different populations or samples and determine the extent of inequality or dispersion. It is particularly useful in studying income inequality, wealth distribution, and other socio-economic variables.

Overall, the Lorenz curve method provides a graphical representation of dispersion and allows for easy comparison and interpretation of the distribution of a variable. It is a valuable tool for researchers and policymakers in understanding and addressing issues related to inequality.