Measures of relative position — A/L Combined Mathematics

Measures of relative position (partition values) divide a sorted frequency distribution into specified fractional proportions: (1) Quartiles divide data into four equal quarters: Lower Quartile Q₁ (25th percentile, position N/4), Median Q₂ (50th percentile, position N/2), and Upper Quartile Q₃ (75th percentile, position 3N/4). For grouped data, quartiles are calculated via: Q_k = L + [(k N / 4 - F) / f_Q] × c (for k = 1, 3); (2) Interquartile Range (IQR) = Q₃ - Q₁ measures the spread of the middle 50% of observations; (3) Semi-Interquartile Range (Quartile Deviation) = (Q₃ - Q₁) / 2; (4) Box-and-Whisker Plot: Summarizes the 5-number summary (Min, Q₁, Q₂, Q₃, Max) and identifies outliers (observations falling beyond Q₁ - 1.5 IQR or Q₃ + 1.5 IQR).

Check before you answer (A/L Applied Maths Paper 2)

1. Grouped Quartile Formulae: Identifying quartile classes from cumulative frequencies and applying the interpolation formula using lower boundaries.
2. Ogive Graphic Readout: Reading Q₁, Q₂, and Q₃ directly from cumulative frequency curves by drawing horizontal lines at N/4, N/2, and 3N/4.
3. Outlier Boundary Detection: Applying 1.5 × IQR thresholds to identify extreme values and plotting them on box-and-whisker diagrams.