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Exercises · Q10

Q.State the relationship connecting the median, quartiles, deciles and percentiles of the same distribution.

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✓ Free question

Because every partition value simply locates a stated FRACTION of the ordered series, values sharing the identical fraction must be identical:

Q2=D5=P50=Median(each locates the 50% point)Q_2 = D_5 = P_{50} = \text{Median} \quad (\text{each locates the } 50\% \text{ point})

Q1=P25(each locates the 25% point)Q_1 = P_{25} \quad (\text{each locates the } 25\% \text{ point})

Q3=P75(each locates the 75% point)Q_3 = P_{75} \quad (\text{each locates the } 75\% \text{ point})

D1=P10, D2=P20, …, D9=P90(each Di shares its fraction with P10i)D_1=P_{10},\ D_2=P_{20},\ \ldots,\ D_9=P_{90} \quad (\text{each } D_i \text{ shares its fraction with } P_{10i})

This relationship holds for EVERY dataset, not just specific examples — it follows purely from the arithmetic of the position fractions, not from any property of a particular distribution's shape.

✓Final answer

Q2 = D5 = P50 = Median; Q1 = P25; Q3 = P75; and Di = P(10i) for every decile.

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