Quantiles

Quantile (or fractile) means a value at or below which a stated fraction of the data lies.

Quartiles divide the distribution into quarters, quintiles into fifths, deciles into tenths, and percentiles into hundredths.

Observations: 8.83, 10.99, 11.92, 12.13, 12.84, 13.60, n = 6, the 75th percentile is

L75=6+175100=5.25.

L₇₅ is between the 5^th and 6^th observations with X₅ = 12.86, X₆ = 13.60. The estimate of the 75th percentile is

P75≈X5+5.25-5X6-X5=12.84+0.2513.6-12.84=13.03

The fourth quintile return for the MSCI World Index is closest to:

A.  20.65%.

B.  26.03%.

C.  27.37%.

[Solutions] B

The fourth quintile is equivalent to the 80th percentile. L₈₀ = (10 + 1) × (80/100) = 11 × 0.8 = 8.8. The 8.8th position would be between the 8th and 9th entries, 20.65% and 27.37%, respectively. Using linear interpolation,

P₈₀ = X₈ + (L_y – 8) × (X₉– X₈)

P₈₀ = 20.65 + (8.8 – 8) × (27.37 – 20.65) = 26.03%.