Measures of relative position — A/L Combined Mathematics

What must I remember about Measures of relative position?

• Measures of Relative Position (Quantiles): Values that divide an ordered distribution into equal proportioned partitions: Quartiles (4 equal parts), Deciles (10 equal parts), and Percentiles (100 equal parts).
• Quartiles: First / Lower Quartile Q1 (25th percentile, separates lowest 25%); Second Quartile Q2 (50th percentile, equals Median M_e); Third / Upper Quartile Q3 (75th percentile, separates lowest 75%).
• Grouped data quartile formulas: Q1 = L1 + [(N/4 - F1) / f1] * c; Q3 = L3 + [(3N/4 - F3) / f3] * c.
• Interquartile Range (IQR) and Semi-Interquartile Range (Quartile Deviation): IQR = Q3 - Q1 (spans central 50% of data); Quartile Deviation QD = (Q3 - Q1) / 2.
• Box-and-Whisker Plot: Graphical 5-number summary: Minimum, Q1, Median (Q2), Q3, Maximum.

Test yourself (1 minute)

1. Outlier detection using 1.5 * IQR rule

   An observation x is considered an Outlier if x < Q1 - 1.5*IQR or x > Q3 + 1.5*IQR.

2. Estimating quantiles from Ogive

   Plot cumulative frequency polygon (Ogive); read x-value corresponding to N/4 on y-axis for Q1, N/2 for Median, and 3N/4 for Q3.

3. Skewness from Quartiles (Bowley's coefficient of skewness)

   Sk = [(Q3 - Q2) - (Q2 - Q1)] / (Q3 - Q1) = (Q3 + Q1 - 2*Q2) / (Q3 - Q1); Sk = 0 for symmetric, Sk > 0 for right-skewed, Sk < 0 for left-skewed.

Practise Measures of relative position questions today

Source: NIE G.C.E. (A/L) Combined Mathematics Resource Book - Applied Mathematics, Unit 8

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Where does Measures of relative position fit in the syllabus?

Year 2 · Term 3