Percentile Ranking

A percentile (or centile) is the value of a variable below which a certain percent of observations fall. So the 20th percentile is the value (or score) below which 20 percent of the observations may be found. The term percentile and the related term percentile rank are often used in descriptive statistics as well as in the reporting of scores from norm-referenced tests.

The 25th percentile is also known as the first quartile(Q1); the 50th percentile as the median or second quartile(Q2); the 75th percentile as the third quartile (Q3).

The percentile rank of a score is the percentage of scores in its frequency distribution that are lower than it. For example, a score that is greater than 75% of the scores of reporting entities is said to be at the 75th percentile.

The mathematical formula is

\frac{\text{cf}_\ell + 0.5 f_i }{N} \times {100%}\

where cf_ℓ is the cumulative frequency for all scores lower than the score of interest, ƒ_i is the frequency of the score of interest, and N is the number of examinees in the sample. If the distribution is normally distributed, the percentile rank can be inferred from the standard score.

Relation between percentile, decile and quartile

• P₁₀ = D₁
• P₂₀ = D₂
• P₂₅ = Q₁
• P₃₀ = D₃
• P₄₀ = D₄
• P₅₀ = D₅ = Q₂ = median
• P₆₀ = D₆
• P₇₀ = D₇
• P₇₅ = Q₃
• P₈₀ = D₈
• P₉₀ = D₉
• P₁₀₀ = D₁₀ = Q₄

Note: One quartile is equivalent to 25 percentile while 1 decile is equal to 10 percentile.

Percentile ranking occurs independently of competitive ranking.