percentile

(noun)

any of the ninety-nine points that divide an ordered distribution into one hundred parts, each containing one per cent of the population

Related Terms

Examples of percentile in the following topics:

  • Measures of Relative Standing

    • The term percentile and the related term, percentile rank, are often used 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), and the 75th percentile as the third quartile (Q3).
    • Percentiles divide ordered data into hundredths.
    • Percentiles are useful for comparing values.
    • Thus, rounding to two decimal places, $-3$ is the 0.13th percentile, $-2$ the 2.28th percentile, $-1$ the 15.87th percentile, 0 the 50th percentile (both the mean and median of the distribution), $+1$ the 84.13th percentile, $+2$ the 97.72nd percentile, and $+3$ the 99.87th percentile.

  • Percentiles

    • Using the 65th percentile as an example, the 65th percentile can be defined as the lowest score that is greater than 65% of the scores.
    • Unless otherwise specified, when we refer to "percentile," we will be referring to this third definition of percentiles.
    • Therefore, the 25th percentile is 5.5.
    • Therefore, the 85th percentile is:
    • Therefore, the 50th percentile is:

  • Normal probability table

    • In other words, Ann is in the 84th percentile of SAT takers.
    • We can use the normal model to find percentiles.
    • A normal probability table, which lists Z scores and corresponding percentiles, can be used to identify a percentile based on the Z score (and vice versa).
    • For instance, the percentile of Z = 0.43 is shown in row 0.4 and column 0.03 in Table 3.8: 0.6664, or the 66.64th percentile.
    • We can also find the Z score associated with a percentile.

  • Graphing the Normal Distribution

    • Percentiles represent the area under the normal curve, increasing from left to right.
    • Each standard deviation represents a fixed percentile, and follows the empirical rule.
    • Thus, rounding to two decimal places, $-3$ is the 0.13th percentile, $-2$ the 2.28th percentile, $-1$ the 15.87th percentile, 0 the 50th percentile (both the mean and median of the distribution), $+1$ the 84.13th percentile, $+2$ the 97.72nd percentile, and $+3$ the 99.87th percentile.
    • Note that the 0th percentile falls at negative infinity and the 100th percentile at positive infinity.

  • Constructing a normal probability plot (special topic)

    • Determine the percentile of each observation in the ordered data set.
    • If the observations are normally distributed, then their Z scores will approximately correspond to their percentiles and thus to the zi in Table 3.16.
    • The zi in Table 3.16 are not the Z scores of the observations but only correspond to the percentiles of the observations.
    • The first observation is assumed to be at the 0.99th percentile, and the zi corresponding to a lower tail of 0.0099 is −2.33.

  • Measures of the Location of the Data

    • The common measures of location are quartiles and percentiles (%iles).Quartiles are special percentiles.
    • The first quartile, Q1 is the same as the 25th percentile (25th %ile) and the third quartile, Q3 , is the same as the 75th percentile (75th %ile).
    • Percentiles are useful for comparing values.
    • The 30th percentile and the 80th percentile for each set.How much data falls below the 30th percentile?
    • Above the 80th percentile?

  • Normal probability examples

    • What is his percentile?
    • Edward is at the 37th percentile.
    • (a) What is his percentile?
    • (b) What is Jim's height percentile?
    • Erik's height is at the 40th percentile.

  • Lab 1: Normal Distribution (Lap Times)

  • Lab 2: Normal Distribution (Pinkie Length)

  • Summary of Formulas

    • To find the kth percentile when the z-score is known: k = µ + ( z ) σ