Descriptive Statistics · Paper 3 — Free Maths AA HL Practice Questions

A researcher claims that neither zone's rainfall data is symmetrically distributed. For each zone, calculate $$d = \frac{(Q_3 - \text{Median}) - (\text{Median} - Q_1)}{Q_3 - Q_1}$$ and the ratio of upper whisker length to lower whisker length. Hence evaluate the researcher's claim, stating the direction of skew for each zone. [5 marks]

A histogram of Zone A's rainfall is constructed using 8 equal-width bins spanning $300\,\text{mm}$ to $800\,\text{mm}$. The total frequency is 100. Assuming rainfall is uniformly distributed within each inter-quartile interval, show that the frequency density of the bin $[487.5, 550)$ is approximately $0.319\,\text{mm}^{-1}$, and hence prove that this frequency density is less than $0.4\,\text{mm}^{-1}$. [3 marks]