Stem and Leaf Plot Stem and Leaf Plot Stem-and-leaf plots are a method for showing the frequency with which certain classes of values occur. You could make a frequency distribution table or a histogram for the values, or you can use a stem-and-leaf plot and let the numbers themselves to show pretty much the same information. For instance, suppose you have the following list of values: 12, 13, 21, 27, 33, 34, 35, 37, 40, 40, 41. You could make a frequency distribution table showing how many tens, twenties, thirties, and forties you have: You could make a histogram, which is a bar-graph showing the number of occurrences, with the classes being numbers in the tens, twenties, thirties, and forties: (The shading of the bars in a histogram isn't necessary, but it can be helpful by making the bars easier to see, especially if you can't use color to differentiate the bars.) The downside of frequency distribution tables and histograms is that, while the frequency of each class is easy to see, the original data points have been lost.
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You can tell, for instance, that there must have been three listed values that were in the forties, but there is no way to tell from the table or from the histogram what those values might have been. On the other hand, you could make a stem-and-leaf plot for the same data : The "stem" is the left-hand column which contains the tens digits. The "leaves" are the lists in the right-hand column, showing all the ones digits for each of the tens, twenties, thirties, and forties. As you can see, the original values can still be determined; you can tell, from that bottom leaf, that the three values in the forties were 40, 40, and 41. Note that the horizontal leaves in the stem-and-leaf plot correspond to the vertical bars in the histogram, and the leaves have lengths that equal the numbers in the frequency table. That's pretty much all there is to a stem-and-leaf plot. You're just listing out how many entries you have in certain classes of numbers, and what those entries are. Here are some more examples of stem-and-leaf plots, containing a few additional details. Complete a stem-and-leaf plot for the following list of grades on a recent test: 73, 42, 67, 78, 99, 84, 91, 82, 86, 94 I'll use the tens digits as the stem values and the ones digits as the leaves. For convenience sake, I'll order the list, but this is not required: 42, 67, 73, 78, 82, 84, 86, 91, 94, 99 To construct a stem plot, the observations must first be sorted in ascending order: this can be done most easily if working by hand by constructing a draft of the stem and leaf plot with the leaves unsorted, then sorting the leaves to produce the final stem and leaf plot. Here is the sorted set of data values that will be used in the following example: 44 46 47 49 63 64 66 68 68 72 72 75 76 81 84 88 106 Learn More Online Tutoring For Free Math.Tutorvista.com
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Next, it must be determined what the stems will represent and what the leaves will represent. Typically, the leaf contains the last digit of the number and the stem contains all of the other digits. In the case of very large numbers, the data values may be rounded to a particular place value (such as the hundreds place) that will be used for the leaves. The remaining digits to the left of the rounded place value are used as the stem. In this example, the leaf represents the ones place and the stem will represent the rest of the number (tens place and higher). The stemplot is drawn with two columns separated by a vertical line. The stems are listed to the left of the vertical line. It is important that each stem is listed only once and that no numbers are skipped, even if it means that some stems have no leaves. The leaves are listed in increasing order in a row to the right of each stem. It is important to note that when there is a repeated number in the data (such as two 72s) then the plot must reflect such (so the plot would look like 7 | 2 2 5 6 when it has the numbers 72 72 75 76).
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Published on May 2, 2012
Stem-and-leaf plots are a method for showing the frequency with which certain classes of values occur. You could make a frequency distributi...