What is the interquartile range in math3/21/2024 ![]() ![]() The Q3 would likewise be calculated to be 79 instead of 79.5, with a final IQR of 17. Thus, in that case, the Q1 list would actually be 55, 58, 59, 62, 67, 67, and 72, leading to a Q1 of 62 (rather than 60.5). In this case, it is common for some mathematicians, when calculating Q1 and Q3 for an even number of entries (such as we did above), to actually include the median as a value in the grouping in order to avoid taking the mean of the sublists. Like many things in statistics, there are often many accepted conventions for how to calculate something. Again, we will find the mean of the two center most entries:įinally, the IQR is found by subtracting #Q3-Q1#: Thus:įor Q2, our list (colored in green above) is 75, 76, 79, 80, 80, and 85. There is an even number of entries in this list, and therefore a common convention to use for finding the median in an even list is to take the two "center most" entries in the list and find their mean. Once we have the median (also sometimes referred to as the 2nd Quartile ), we can determine the Q1 and Q3 by finding the medians of the lists of values below and above the median, respectively.įor Q1, our list (colored in blue above) is 55, 58, 59, 62, 67, and 67. ![]() In our sorted list, we can see that the value 72 has exactly 6 values less than it and 6 values greater than it: For lists with an odd number of entries, this is easy to do as there is a single value for which an equal number of entries are less than or equal and greater than or equal. The median is generally known as the number is the "center" of the ascending ordered list of values. Semi-interquartile range is one-half the difference between the first and third. Data that is more than 1.5 times the value of the interquartile range beyond the quartiles are called outliers. The interquartile range (IQR) is the difference between the 3rd Quartile value (Q3) and the 1st Quartile value (Q1) of a set of values. Interquartile range Q3 Q1 In the above example, the lower quartile is 52 and the upper quartile is 58.
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