1 Percentiles

2 Seems like on a standardized test we don’t care much about the test score as much as the percentile. (OK not always – ACT, for example.) The percentile tells us what percent of the test takers had this score or a lower score. Some ideas to consider to find percentiles. 1) We mention the idea called integers. An integer is a whole number, you know, one without fractions or decimals. 2) The data should be sorted, or arranged, in ascending order (lowest to highest.) 3) After the data has been sorted, visualize the data in a row from left to right. In fact, think of each number as being in a room and the number of the room will be called its position. So the lowest number is in the first position. The positions are made up of the integers. The last position is the number of observations.

3 On this last point let’s be clear on something. The data values come from the subjects in the study and when the data is sorted the values will have another number called the position. Easy example: Parker’s wake up time the last four days: 7:02, 5:15, 6:24, and 6:10. Sorted – 5:15, 6:10, 6:24, 7:02 Position On the next screen let’s see how to find percentiles and we will assume the data has already been sorted. We will talk about the p th percentile.

4 Let p = the percentile of interest, n = the number of data points or observations, then i = (p/100)n is an index number (a fancy name for a handy little device) we will use to find p th percentile. IF a) i is not an integer, round up to the next integer. In other words, the next integer higher than i is the position of the p th percentile. b) i is an integer, the p th percentile is the average of the values in the i and i + 1 positions.

5 An example: last 10 golf scores for 18 holes, sorted: 82, 83, 84, 85, 85, 88, 90, 90, 93, 95 To find the 50 th percentile score, first find i. i = (50/100)10 = 5. So the 50 th percentile is the average of the values in the 5 th and 6 th positions – 85 and 88, for an average of 86.5 Thus 86.5 is the 50 th percentile. Note the 50 th percentile is the median we saw before. Half the values are below this value and half are above this value. To find the 25 th percentile, we take i = (25/100)10 = 2.5. So the 25 th percentile is the value in the 3 rd position – % of the values are less than or equal to this.

6 Quartiles Quartiles are just special percentiles. The 25 th percentile is the 1 st quartile, the 50 th percentile is the 2 nd quartile (and also called median) and the 75 th percentile is the 3 rd quartile. What is most important here, I think, is that you understand the meaning of a percentile and the special percentiles called quartiles.