Interquartile range

The lengths, in cm, of 9 daschunds are 45, 47, 48, 49, 50, 51, 52, 53, and 60 The median is 50 Q1=(47+48)/2, Q3=(52+53)/2 More on reddit.com

Is an IQR the amount of distance or range that the middle 50% of the data set can vary from the median? No It's just the distance between the 25th and 75th percentile. Sample IQR is the range of the middle half of the data. Does this mean that a data point from the middle 50% can vary from the median by up to $38,000 in either direction of the median? No. the spread of the middle 50% of the data can be up to $38,000. Nearly; the range of the middle 50% is 38000. You seem to be thinking about differences between values that are not at the quartiles, but somehow values in between them. [However, for sample IQR, vagaries of the calculation in finite samples and the specific definition of sample quartile you use can have some impact; e.g. you may need to include one or both of the quartiles to get to 50%, and in some cases the quartiles may fall between data points in which case there could be a slightly smaller interval that also includes half. Sample quantiles are tricky to define and you may want slightly different properties to apply in different situations, which is why there's so many definitions). R has 9 different quantile definitions available in the function quantile, without considering Tukey's definition of "hinge" in boxplots.] what would be the boundary values that the middle 50% of the data falls in between The quartiles that you calculated the range between. What does IQR stand for? It's the inter-quartile range, literally "the distance between the quartiles"; the name tells you exactly how it is obtained. So the boundary values are the first and third quartiles, the very things you take the difference of (Q3-Q1) to get the range between them -- the inter-quartile range (IQR) -- in the first place More on reddit.com

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