Which approach would be inappropriate when comparing means by location?

• A. Using grouped statistics by month or location and comparing the groups.
• B. Taking the overall mean across all locations and comparing it to per-location means.
• C. Plotting histograms for each location and visually comparing.
• D. Computing the mean for only one randomly selected location.

Answer: (B)

When comparing means by location, you want to respect the fact that data come in groups and that each location may have its own typical value and variation. Using the overall mean across all locations as a baseline and then comparing each location’s mean to that single grand average folds together all locations into one number. That can hide real differences between locations and can be influenced by how many observations come from each location. In short, the grand mean doesn’t represent any actual location, so comparing location-specific means to it can mislead you about where differences really lie.

The other approaches keep the location structure intact or provide a clear view of differences: grouping data by location and comparing those group means directly shows how locations differ; plotting histograms for each location lets you see differences in the shapes and spread of the data, which informs whether comparing means is meaningful; though using the mean from a single randomly chosen location would be weak for making broad conclusions, it at least avoids averaging across locations entirely and highlights that a single location isn’t representative of the whole set.