Statistics
NCEA Level 1 Statistics assesses the statistical enquiry cycle: posing a question, collecting and cleaning data, displaying and summarising distributions, and making evidence-based conclusions. You must interpret data in context and justify choices, not just calculate.
Core rules and concepts
- Classify variables as categorical (nominal or ordinal) or numerical (discrete or continuous).
- Summarise centre and spread: mean and standard deviation for roughly symmetric data; median and interquartile range (IQR) for skewed data or data with outliers.
- Five-number summary: minimum, lower quartile, median, upper quartile, maximum. IQR = upper quartile − lower quartile.
- An outlier is often defined as a value below Q1 − 1.5 × IQR or above Q3 + 1.5 × IQR.
- In scatterplots, describe trend, strength, and form. Correlation does not prove causation.
- Probability from data uses relative frequency = count ÷ total. Expected number = probability × number of trials.
Worked example
Eight scores: 12, 15, 15, 18, 20, 21, 24, 35. Median = (18 + 20)/2 = 19. Lower quartile = median of lower half (12, 15, 15, 18) = 15. Upper quartile = median of upper half (20, 21, 24, 35) = 22.5. IQR = 22.5 − 15 = 7.5. Upper fence = 22.5 + 1.5 × 7.5 = 33.75. Since 35 > 33.75, 35 is an outlier. Report the median as 19 and the IQR as 7.5, and note the outlier rather than letting it distort the mean.
Traps
- Giving a mean for skewed data without acknowledging the outlier.
- Confusing the median with the midrange, or averaging the wrong pair.
- Describing correlation as proof that one variable causes another.
- Reading histogram bins as exact values.
- Ignoring sample size when comparing groups.