What transformation would be best used to stabilize variance and make the data more normal distribution-like?

The logarithmic transformation is a powerful technique used to stabilize variance and help make the data more closely resemble a normal distribution. This approach works particularly well for datasets with exponential growth patterns or when the data exhibits skewness, especially right skewness. By applying the logarithmic function, you compress the range of high values and expand the range of low values, which tends to reduce the influence of outliers and bring the overall data distribution closer to normality.

In contrast, normalization, standardization, and min-max scaling are methods that do not specifically target variance stabilization or normality. Normalization typically rescales data to fit within a specific range, often between 0 and 1, without addressing the distribution's shape. Standardization (z-score normalization) shifts the data to have a mean of 0 and a standard deviation of 1 but does not inherently alter the overall distribution to resemble normality. Min-max scaling rescales features to a common range, which is useful for certain algorithms but does not directly help in achieving a normal distribution. Therefore, the logarithmic transformation stands out as the most effective approach for stabilizing variance and making the data distribution more normal-like.