However, we have yet to determine if this temperature is a major outlier, so let's not draw any conclusions until we do so. In our data set, only the temperature of the oven - 300 degrees - lies outside this range and thus may be a mild outlier.Thus, the boundaries of our inner fence are 67.75 and 73.75.We add this number to Q3 and subtract it from Q1 to find the boundaries of the inner fences as follows: In our example, the interquartile range is (71.5 - 70), or 1.5.The two resulting values are the boundaries of your data set's inner fences. Then, add the result to Q3 and subtract it from Q1. To find the inner fences for your data set, first, multiply the interquartile range by 1.5. X Research source A point that falls outside the data set's inner fences is classified as a minor outlier, while one that falls outside the outer fences is classified as a major outlier. Outliers are identified by assessing whether or not they fall within a set of numerical boundaries called "inner fences" and "outer fences". So, the median for our data set is the average of these two points: ((70 + 71) / 2), = 70.5.įind the "inner fences" for the data set. The middle 2 terms are points 6 and 7 - 70 and 71, respectively. However, if the two middle points are the same number, the average, obviously, will be this number as well, which is also OK. Don't be confused by data sets with even numbers of points - the average of the two middle points will often be a number that doesn't appear in the data set itself - this is OK.Note that, when calculating outliers, the median is usually assigned the variable Q2 - this is because it lies between Q1 and Q3, the lower and upper quartiles, which we will define later. However, if there are an even number of points, then, since there is no single middle point, the 2 middle points should be averaged to find the median. X Research source If the data set contains an odd number of points, this is easy to find - the median is the point which has the same number of points above as below it. The median of a data set is the data point above which half of the data sits and below which half of the data sits - essentially, it's the "middle" point in a data set. If 11 of the objects have temperatures within a few degrees of 70 degrees Fahrenheit (21 degrees Celsius), but the twelfth object, an oven, has a temperature of 300 degrees Fahrenheit (150 degrees Celsius), a cursory examination can tell you that the oven is a likely outlier.Ĭalculate the median of the data set. Let's consider a data set that represents the temperatures of 12 different objects in a room.If, for instance, the majority of the points in a data set form a straight line, outlying values will not be able to be reasonably construed to conform to the line. X Research source If the data set is expressed visually on the graph, outlying points will be "far away" from the other values. It's usually easy to detect this on data tables or (especially) on graphs. Generally speaking, outliers are data points that differ greatly from the trend expressed by the other values in the data set - in other words, they lie outside the other values. Before deciding whether or not to omit outlying values from a given data set, first, obviously, we must identify the data set's potential outliers. Learn how to recognize potential outliers. This article has been viewed 1,239,530 times. This article received 21 testimonials and 80% of readers who voted found it helpful, earning it our reader-approved status. WikiHow marks an article as reader-approved once it receives enough positive feedback. There are 8 references cited in this article, which can be found at the bottom of the page. Additionally, David has worked as an instructor for online videos for textbook companies such as Larson Texts, Big Ideas Learning, and Big Ideas Math. After attaining a perfect 800 math score and a 690 English score on the SAT, David was awarded the Dickinson Scholarship from the University of Miami, where he graduated with a Bachelor’s degree in Business Administration. With over 10 years of teaching experience, David works with students of all ages and grades in various subjects, as well as college admissions counseling and test preparation for the SAT, ACT, ISEE, and more. David Jia is an Academic Tutor and the Founder of LA Math Tutoring, a private tutoring company based in Los Angeles, California. This article was co-authored by David Jia.
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