Percentiles give information about how an individual statistic compares to a broader sample of statistics. A common example is college entrance exam scores. An individual score in the 90th percentile means that 90 percent of the participants who took the exam scored at or under that person's score. It is not a measure of the individual score, but of placement of that score in comparison to others. Calculating this number is relatively easy, especially if data can be easily ordered from lowest to highest.
Two types of percentiles can be calculated. The first type measures what percent of all data in a sample is at or below a chosen point. The second type only measures the percentage of the data that is below a chosen statistic. Both types require that all data in a sample be ordered from lowest to highest. Once this is complete, the first type of percentile can be calculated by counting the number of data points below a chosen point. Then, take half the number of data points that equal the chosen point. and add that to the number below the point. Divide this sum by the total number of points in the entire sample, and then multiply by 100 to convert to a percent. The second type of percentile is easier to calculate. Simply divide the number of points below the chosen point by the total number of points in the sample, and then multiply by 100.
Consider a classroom of ten students of the following weights, in pounds: 75, 80, 85, 90, 95, 95, 100, 100, 105, 105. From this, students can easily discover what percentile a student weighing 100 pounds falls into. For the first type of percentile, which measures the percentage of students at or below 100 pounds, we add 6 -- the number of students under 100 pounds-- to half of 100 -- the number of students at 100 pounds. Since 10 is the total number of students, divide the sum by 10. Multiplied by 100, the 100-pound students fall into the 70th percentile. The second type of percentile, which only measures students who weigh less than 100 pounds, the calculation is just 6 divided by 10 and multiplied by 100: they are at the 60th percentile.
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