ConceptProbability & Statistics
← All conceptsDescriptive statistics
mean, median, mode, variance
10 ways this goes wrong. Each one is a named misconception the questions are built to catch.
- Extremes not trimmedForgets to remove highest and lowest before computing trimmed mean/variance, or divides by the untrimmed count.→
- Mean ignores frequenciesComputes the mean without weighting by frequencies/group sizes.→
- Median without sortingReads the median without ordering the data first.→
- Mode vs median confusedConfuses the most-frequent value (mode) with the positional median.→
- Outlier must shift medianAssumes the median must move (or variance could shrink) when one extreme value is added.→
- Plain average of two meansTakes the simple average of two group means instead of weighting by group sizes.→
- Variance changes under +constantThinks standard deviation/variance changes when a constant is added to every value (or that the mean is unchanged).→
- Variance formula misstatedDivides by the wrong n or omits the mean-deviation squaring in the variance formula.→
- Variance inferred from meanBelieves variance can be deduced from the mean, or that a larger mean implies larger variance.→
- Wrong statistic for the questionChooses mean/variance when a positional cutoff (median) or ranking is actually required.→
