![]() ![]() So really we are first translating x by -min, scaling it to the correct factor, and then translating it back up to the new minimum value of a. You might also notice that (b-a)/(max-min) is a scaling factor between the size of the new range and the size of the original range. You can verify that putting in min for x now gives a, and putting in max gives b. ![]() Now if instead we want to get arbitrary values of a and b, we need something a little more complicated: (b-a)(x - min) So we need to do a translation and a scaling. Range is an easy to calculate measure of variability, while midrange is an. So we'll have to scale it: x - min max - minį(x) = - => f(min) = 0 f(max) = - = 1 The midrange is the average of the largest and smallest data points. But putting in max would give us max - min when we actually want 1. Putting min into a function and getting out 0 could be accomplished with f(x) = x - min => f(min) = min - min = 0 In your case, a would be 1 and b would be 30, but let's start with something simpler and try to map into the range. You're looking for a (continuous) function that satisfies f(min) = a So range and mid-range.Let's say you want to scale a range to. In particular, the range is a linear function of order statistics, which brings it into the scope of L-estimation. Obviously, you couldĪlso look at things like the median and the mode. The range is a specific example of order statistics. The arithmetic mean, where you actually take So this is going to be what? 90 plus 60 is 150. The mid-range would be theĪverage of these two numbers. With the mid-range is you take the average of the One way of thinking to some degree of kind ofĬentral tendency, so mid-range. The tighter the range, just to use the word itself, of The larger the differenceīetween the largest and the smallest number. See, if this was 95 minus 65, it would be 30. Want to subtract the smallest of the numbers. Largest of these numbers, I'll circle it in magenta, The way you calculate it is that you just So what the range tells us isĮssentially how spread apart these numbers are, and Mid-range of the following sets of numbers. In statistics you're given the numbers and you have to figure out what kind of equation they describe. In ordinary math you're given the relationship of the equation and you just have to plug in the numbers. Do people going to the beach make the temperature go up? Or is it the other way around? In this example it is obvious, but lots of times it isn't. Sometimes there is a relationship, sometimes there is not, and even when there is a relationship it isn't aways easy to figure out what it is. In statistics you're basically given two or more variables (x, y, etc) and you have to figure out if there is a relationship among them. In ordinary mathematics you're given a relationship in the form of an equation (x+y = z) that you can then plug numbers into and get an answer. In this case there obviously is, but in other examples the relationship isn't so obvious. For example, if the temperature goes up on the thermometer, and you count more people going to the beach, then you might want to determine whether there is a relationship between the two things. Statistics attempt to establish the relationship between one or more measured things. ![]()
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