When ranking numbers, such as test scores or the length of elephant tusks, it can be helpful to conceptualize one rank in relation to another. For example, you might want to know if you scored higher or lower than the rest of your class or if your pet elephant has longer or shorter tusks than most of the other pet elephants on your block. One way to conceptualize a ranking system is through the use of quartiles, which represent three divides within your data that splits the data into four equal parts.
Rank your values in order from lowest to highest; you will use this ranked value order in all of the different methods for computing quartiles. The first method for computing quartiles is to divide your newly ordered dataset into two halves at the median.
Find the median, or middle value, of your dataset. For example, if your dataset is (1, 2, 5, 5, 6, 8, 9), the median is 5 because that is the middle value. This middle value represents your second quartile, or 50th percentile. Fifty percent of your values are higher than this value, and 50 percent are lower.
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Draw a line at the median to separate the lower half of your data, which is now (1, 2, 5), and the upper half of your data, which is (6, 8, 9). The first quartile value, or 25th percentile, is the median of the lower half, which is 2. The third quartile, or 75th percentile, is the median of the upper half, which is 8. So you know that about 25 percent of your numbers are lower than 2, half of your numbers are 5 or lower, and about three-quarters of your values are lower than 8.
Find the difference between your upper quartile, or 75th percentile, and your lower quartile, or 25th percentile. Using the dataset (1, 2, 5, 5, 6, 8, 9), your interquartile range is the difference between 8 and 2, so your interquartile range is 6.