Welcome to my new feature - the Statistics Term of the Day. I'll try to start by focusing on terms that you non-statisticians out there are likely to see on your - or your child's - test score report. I'll try to keep the order somewhat logical but these early terms might be a tad out of order. I'll put stats terms that I've either covered, or (since this is the first installment), plan to cover, in bold.
If it gets heinously boring, tell me.
Today the term is percentile. Put simply, the percentile is a value ranging from 1 to 100 (so it looks like a percentage) that indicates the percent of the distribution that lies below it. Often test scores are accompanied by a percentile; e.g., "This student's reading score is at the 98th percentile." That value is the percent of examinees in some reference group (often, the examinees who have taken the exam in the years prior) below the given score.
If you are at the 98th percentile, your percentile rank is 98. You have scored higher than 98 percent of some reference group of examinees. the College Board provides percentiles so that examinees can see how they did on the SAT as compared to examinees who took it in previous years.
Another phrase you might see with percentiles is cumulative frequency distribution or cumulative percentage. Cumulative in this case means increasing by successive additions; a cumulative frequency distribution is created by adding up all the ranked values in a distribution. Cumulative percentages are used to create percentiles; in order to know that score X is at the 98th percentile, the percents of all scores below score X had to be summed.
The 50th percentile is also known as the median, which is the measure of central tendency that divides the sample (or distribution) in half. Fifty percent of observations lie above the median, and fifty percent below. The median is not the same as the mean, which is the mathematical average or center of a sample or distribution. When a distribution is non-normal or skewed, the median is often the correct measure of central tendency. This is why you often see median, not mean, incomes reported, so that the few millionaires in the bunch don't confuse the analyses.
Posted by kswygert at March 7, 2005 07:56 PM