![]() But really, in your head, you know they should be saying “half of all drivers are below median“.įigures like housing prices and incomes are often given in terms of the median, since we want an idea of the middle of the pack. ![]() Some jokes run along the lines of “Half of all drivers are below average. Not as well-known when you say “median”, people may think you mean “average”.Can be harder to calculate: you need to sort the list first.Splits data into two groups, each with the same number of items.Handles outliers well - often the most accurate representation of a group.Outliers like 100 only tug the median along one item in the sorted list, instead of making a drastic change: the median of 1 2 3 4 is 2.5. If there’s two middle numbers (even number of items), just take their average. The median solves this problem by taking the number in the middle of a sorted list. The average has been pulled up by 100, an outlier. We’re more likely to get a number closer to 3 than to 22. And although the average (22) is somewhere in the “middle”, 22 doesn’t really represent the distribution. Humor me for a second: what’s the “middle” of these numbers? But doesn’t the average (arithmetic mean) imply the same thing? What gives? Unfortunately, there’s always those 20% of situations where the average doesn’t quite fit. The arithmetic mean works great 80% of the time many quantities are added together. The average of 100, 200 and -300 is 0, which is misleading. The average can be skewed by outliers - it doesn’t deal well with wildly varying samples.It’s intuitive - it’s the number “in the middle”, pulled up by large values and brought down by smaller ones.Easy to calculate: just add and divide.It works well for lists that are simply combined (added) together.In this case, we’d swap in three people weighing 200 lbs each, and nobody would be the wiser. The real question is “If you replaced this merry group with 3 identical people and want the same load in the elevator, what should each clone weigh?” Let’s say you weigh 150 lbs, and are in an elevator with a 100lb kid and 350lb walrus. The arithmetic mean is the most common type of average: But the calculation depends on how the items in the group interact. One goal of the average is to understand a data set by getting a “representative” sample. If I could throw away my data and replace it with one “average” value, what would it be? The average is the value that can replace every existing item, and have the same result. I’m a fan of taking multiple viewpoints, so here’s another interpretation of the average: To most of us, it’s “the number in the middle” or a number that is “balanced”. Let’s step back a bit: what is the “average” all about? ![]() ![]() Read on to understand the many uses of this statistical tool. Hint: It’s not 45 mph, and it doesn’t matter how far your commute is. Quick quiz: You drove to work at 30 mph, and drove back at 60 mph. The type of average to use depends on whether you’re adding, multiplying, grouping or dividing work among the items in your set. The average is a simple term with several meanings. ![]()
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