Statistics
What this domain tests
Statistics questions ask you to read data summaries and reason about center, spread, and shape. You need mean, median, mode, range, and a working sense of how outliers and skew affect each measure.
Core concepts
- Mean = sum ÷ count. It is sensitive to outliers.
- Median = middle value when ordered (average the two middle values for an even count). It resists outliers.
- Mode = most frequent value; a data set may have none or several.
- Range = max − min. It uses only two points.
- Skew: in a right-skewed (positively skewed) distribution, mean > median; in a left-skewed one, mean < median.
- Standard deviation measures typical distance from the mean; adding the same constant to every value leaves it unchanged, but multiplying scales it.
Traps
- Forgetting to order the data before finding the median.
- Assuming the mean and median are equal-only true for symmetric data.
- Confusing "range" with "spread" broadly; range ignores the middle entirely.
- Misreading a table: check whether a column is a count or a percent.
Worked example
Data: 4, 6, 6, 8, 21. Sum = 45, count = 5, mean = 9. Ordered median = 6. Mode = 6. Range = 17. The single value 21 pulls the mean above the median, signaling right skew. If asked which measure better represents a "typical" value here, the median (6) is the better choice because it is not inflated by the outlier.
Rule of thumb
When a data set has an outlier or strong skew, prefer the median; when data are symmetric and clean, the mean uses all the information.