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Percentiles A percentile is a measure of relative standing, meaning we get information about the position of a value relative to the rest of the data set. 1 An example: last 10 golf scores for 18 holes, sorted: 82, 83, 84, 85, 85, 88, 90, 90, 93, 95 1 2 3 4 5 6 7 8 9 10 Here I have an example where I wrote down the last 10 golf scores I had. Note that I have sorted the scores from low to high score (although that is not the order I shot them – but for what I want to do next I need to have the data sorted from low to high – ascending order). Below each score I put the “location” of the score in the ascending order. 2 Here is an approximation method to get percentiles. Let p = the percentile of interest, n = the number of data points or observations, then Lp = (n + 1)(p/100)n is a location index number (a fancy name for a handy little device) we will use to find pth percentile. Now, if n = 10 and if we want the 25th percentile the location index is Lp = (10 + 1)(25/100) = 11(.25) = 2.75. In my example data points have locations with whole numbers. The location index of 2.75 is between 2 and 3. The 25th percentile value will be 75% of the way between the 2nd and 3rd number. 3 The 2nd number is 83 and the third number is 84. To get the 25th percentile number take the lower number, 83 and add .75 of the difference between the 2nd and 3rd numbers: 83 + .75(84 – 83) = 83.75. Note if the index is a whole number the value in that location is the percentile of interest. The 50th percentile here is found by: Lp = (10 + 1)(50/100) = 5.5 or half the way between the 5th and 6th numbers. So, 85 + .5(88 – 85) = 86.5 is the 50th percentile. 4 Quartiles Quartiles are just special percentiles. The 25th percentile is the 1st quartile, the 50th percentile is the 2nd quartile (and also called median) and the 75th percentile is the 3rd quartile. What is most important here, I think, is that you understand the meaning of a percentile and the special percentiles called quartiles. 5 special percentiles •The 25th and 75th percentiles are called the 1st and 3rd quartiles(Q1 and Q3), respectively. They are just the medians of the lower and upper halves of the arranged values. The following is a visual to see the percentiles. lowest 25% of observations first quartile is a value next 25% next 25% median is a value highest 25% third quartile is a value number line where we measure values of the variable Interquartile range •Variation can be indicated by the interquartile range, IQR = Q3 - Q1. The smaller the IQR, the closer Q3 and Q1 are in the graph and thus the lower the spread! •Hey, please check out the box plot, or what is sometimes called the box and whiskers plot in the text. I know you will!