When might you apply a log transformation to data before summarizing with mean and standard deviation?

• A. When data are perfectly normal
• B. When data are categorical
• C. When data are positively skewed or have heteroscedastic variance to stabilize variance and normalize
• D. When sample size is large

Answer: (C)

When data are positively skewed or show heteroscedasticity (the spread grows with the level of the data), applying a log transformation helps. The log compresses large values and stretches small ones, which tends to pull the right tail in and make the spread more uniform across the range. This makes the distribution on the transformed scale closer to normal and stabilizes variance, so the mean and standard deviation computed after the transformation provide a more reliable summary. If the data are already roughly normal, a log transform isn’t needed and can make interpretation less clear. Categorical data aren’t summarized with a mean and standard deviation anyway, and simply having a large sample size doesn’t justify transforming the data.