#math-shit

A stem-and-leaf graph, also called a stemplot, is a way to represent the distribution of numeric data. It was invented by John Tukey, a mathematician, and is a quick way to picture data for numbers that are greater than 0. I'll explain using an example. Suppose you have the following set of numbers (they might represent the number of home runs hit by a major league baseball player during his career). 32, 33, 21, 45, 58, 20, 33, 44, 28, 15, 18, 25 The stem of a stemplot can have as many digits as needed, but the leaves should contain only one digit. To create a stemplot to display the above data, you must first create the stem. Since all of the numbers have just two digits, start by arranging the tens digits from smallest to largest. To create the leaves, draw a vertical bar after each of the tens digits and arrange the ones digits from each number in the data set in order from smallest to largest. If there are duplicate numbers, like 33, list each one. 1|58 2|0158 3|233 4|45 5|8 The shape of the resulting display looks something like a bar graph oriented vertically. By examining the stemplot, you can determine certain properties of the data. You can find the median by counting from either end of the stemplot until you find its center. Here, since there are 12 numbers, the center lies between 28 and 32. The median is the average of the two data points: (28+32)/2 = 30.) You can also determine if there is a mode in the data set by looking at the plot. Here, the number 33 is the mode since it is the only value that occurs more than once. If your data contain three digit numbers (like batting averages, for example), you can use the same technique. For example, let's assume the data are 298, 303, 285, 311, 225, 315, 250, 305 Ignore the ones digits in each number (these will be the leaves) and look at the remaining two digits in each number (the hundreds and tens digits). The stem will begin at 22 because the smallest number in the data set is 225. The stem will end at 31 because the largest number is 315. Include the two-digit numbers between 22 and 31 in the body of the stem. Once you have the stem, then list the ones digits in each number after the corresponding two-digit number before it. The stemplot will look like this, with no leaves after the numbers without a corresponding value. 22|5 23| 24| 25|0 26| 27| 28|5 29|8 30|35 31|15 If these data represent the batting averages for a particular player, this display indicates that he has had a very successful career - most of his averages are clustered between 280 and 320.

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