PERCENTILE AND PERCENTILE RANK



Percentile and Percentile Rank

Percentiles: The quartiles and the median are special cases of percentiles for a data set. In general, the kth percentile is a number that has k% of the data values at or below it and (100 – k)% of the data values at or above it. The lower quartile, median, and upper quartile are also the 25th percentile, 50th percentile, and 75th percentile, respectively. If you are told that you scored at the 90th percentile on a standardized test (like the SAT), it indicates that 90% of the scores were at or below your score, while 10% were at or above your score.

There probably have been several instances in your life where information about your percentile ranking on a particular variable has been provided to you. For example, you may have been told that your Verbal SAT score was at the 80th percentile of all Verbal SAT scores, or that your height was at the 50th percentile for individuals of your sex and age. Remember that the kth percentile for a data set is a number that has k% of the data values at or below it. The same definition holds true for random variables. If your Verbal SAT score was at the 80th percentile, then your score was higher than the scores of 80% of the other test takers (and lower than 20%).

In some problems, we may want to know what value of a variable defines a specified percentile ranking. We may, for example, want to know what IQ score is the 98th percentile, or what pulse rate is the 25th percentile of pulse rates for your gender. You should notice that the word percentile refers to the value of a variable, while percentile ranking refers to the proportion below that value. For instance, if the 25th percentile of pulse rates is 64 beats per minute, then 25% of pulse rates are below 64 and 75% are above 64. The percentile is 64 beats per minute, and the percentile ranking is 25% or .25.

In probability terms, the percentile rank for the value of a variable corresponds to the cumulative probability for that value. For example, the 25th percentile of pulse rate is the pulse rate for which .25 is the cumulative probability (area to the left under the normal curve).

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