Statisticians point out that it’s often useful to “chunk” data to understand it.\u00a0 What does it mean to “chunk” data? It means dividing a long list into smaller chunks so that, with a few well-chosen numbers, we can get a sense of the layout of the list.<\/p>\n
The fundamental “chunking” number is the median.\u00a0 The median is the middle of the list: that is, it divides the list into two chunks: an upper list and a lower list.\u00a0 This one number, the median, tells you both the maximum of the lower list and the minimum of the upper list.<\/p>\n
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Quartiles extend this idea.\u00a0 First, find the median, which divides the entire list into a “top 50%” list and a “bottom 50%.”\u00a0 Now, find the medians of each one of these lists.\u00a0 The median of the “bottom 50%” called Q1<\/sub>, the first quartile<\/strong>.\u00a0 The median of the “top 50%” is called the third quartile<\/strong>.\u00a0 The quartiles are called “quartiles” because the two quartiles and the median nicely divide the list into four equal chunks.<\/p>\n Notice that, we don’t use the term “second quartile” because the median plays the role of the second quartile.<\/p>\n <\/p>\n Often, statisticians are bothered by outliers, that is, extreme high or low values.\u00a0 An outlier is a member on the list who is not representative of most of the list.\u00a0 In the list of household incomes in the US, the incomes of Bill Gates and Warren Buffett are not representative of the rest of us: they are outliers.\u00a0 Outliers, by definition, will always be at the very top or the very bottom of a list.<\/p>\n Notice that both the “top 50%” and the “bottom 50%” will necessarily contain any outliers.\u00a0 Would it be possible to talk about a “half” of the population that definitely contains no outliers?\u00a0 Well, instead of the “top 50%” or the “bottom 50%”, we could take the “middle 50%<\/strong>“.\u00a0 What’s that?\u00a0 Well, suppose we look at all the folks between the first quartile and third quartile.\u00a0 We know that a quarter of the population is between the first quartile and the median, and a quarter between the median and the third quartile, so between the first quartile and the third quartile is 50% of the population, and it’s the 50% that’s in the middle of the population.\u00a0 This is called the interquartile range<\/span><\/strong>: the set of data entries from the first quartile to the third quartile.\u00a0 It’s a big deal because it’s not the upper half or lower half but rather the middle half<\/strong> of the data.\u00a0 For this reason, statisticians feel it gives a very good representation where the typical data lie.<\/p>\n <\/p>\n Consider the geographic size of countries.\u00a0 On planet Earth, what is the size of a typical country?\u00a0 Well, if we list the countries and their areas, we find the maximum is Russia (16,995,800 sq km) and the minimum is the Holy See (0.44 sq km).\u00a0 Obviously, neither one of those is typical of the area of a country.<\/p>\n The median value on the list is 50660 sq km (Costa Rica).\u00a0 So that’s interesting: half the countries on Earth have more area than Costa Rica, and half have less.\u00a0 Incidentally, the US State of West Virginia is slightly bigger than this, so little old West Virginia has more area than half the countries on Earth.\u00a0 Who would have thought that? \u00a0\ud83d\ude42<\/p>\n The third quartile is 325360 sq km (Vietnam) and the first quartile is 572 sq km (the Isle of Man).\u00a0 So, even within the interquartile range, there’s huge variation from 572 up to 325360.\u00a0 Still, we can say half the countries on Earth have more area than the Isle of Man but less area than Vietnam.\u00a0 That’s where the middle 50% lies.\u00a0 That would be, in many ways, the most representative range for the size of a “typical” country.<\/p>\n <\/p>\n","protected":false},"excerpt":{"rendered":" Statisticians point out that it’s often useful to “chunk” data to understand it.\u00a0 What does it mean to “chunk” data? It means dividing a long list into smaller chunks so that, with a few well-chosen numbers, we can get a sense of the layout of the list. The fundamental “chunking” number is the median.\u00a0 The […]<\/p>\n","protected":false},"author":26,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[39,25],"tags":[],"ppma_author":[12267],"class_list":["post-8843","post","type-post","status-publish","format-standard","hentry","category-data-analysis","category-math"],"acf":[],"yoast_head":"\n\n
The Interquartile Range<\/h2>\n
An Example with Real Data<\/h2>\n