Statistics & Data Interpretation at the 700-800 Level

At this level the questions are about center and spread: mean, median, standard deviation. You will almost never be asked 'what is the mean?' You will be asked what happens to the mean, or what the mean forces some other value to be.

The single most useful sentence in the topic is $\text{sum} = n \times \text{mean}$. Every hard item that mentions a mean is really handing you a total — convert immediately, edit the total, and divide once at the end. That one move handles missing values, removed values, corrected entries, and added values without ever averaging a list twice.

Weighted means generate their own family: the average of two averages is almost never the combined average. The lever shortcut says group sizes are proportional to the opposite distances from the combined mean, and writing that ratio backwards is the most common error on the archetype. Median behaves independently of mean — adding or removing one value flips a list between odd and even counts, so compute both statistics twice rather than predicting one from the other. Transformations: $ax + b$ moves the center to $a(\text{center}) + b$ but scales spread by $|a|$ alone.

The recurring failure is the intermediate value — you compute the new mean correctly, and the question asked for the change.