For example, the column at x=2 is 5 units high, indicating that there are 5 students with 2 siblings. A histogram for this data is shown below.Įach number on the x−axis has an associated column, whose height shows how many students have that number of siblings. When the data we are representing falls into well defined categories (such as the integers 1, 2, 3, 4, 5 & 6) it is more appropriate to use a histogram to display that data. In this case, where the data points are all integers, it’s wrong to suggest that the function is continuous between the points! For example, the continuous line joining the number of students with one and two siblings makes it look like we know something about how many students have 1.5 siblings (which of course, is impossible). While this diagram does indeed show the data, it is somewhat misleading. Now we could use this table as an (x,y) coordinate list to plot a line diagram like this one: Here is the table again, but this time we will use the word frequency as a header to indicate the number of times each value occurs in the list. We were able to organize the data into a table. Look again at the example of the algebra students and their siblings. (Using our formula from earlier, (43+1)/ 2=22.) So the median is 37. The median is the middle value since there are 43 data points, the median is the 22nd value. The mode is now apparent-there are 4 zeros in a row on the 4-branch, so the mode is 40. In order to correctly determine the median and the mode, it is helpful to construct a second, ordered stem and leaf plot, placing the leaves on each branch in ascending order You can see immediately that the interval with the most number of passengers is the 40-49 group. We then go through the data and fill out our plot: Since all the values fall between 1 and 84, the stem should represent the tens column, and run from 0 to 8 so that the numbers represented can range from 00 (which we would represent by placing a leaf of 0 next to the 0 on the stem) to 89 (a leaf of 9 next to the 8 on the stem). The first step is to determine a sensible stem. The ages for the passengers are shown below. While traveling on a long train journey, Rowena collected the ages of all the passengers traveling in her carriage. In that case, no additional information could be gained from a stem-and-leaf plot. For example, with the data above about students’ siblings, all the data points would occupy the same stem (zero). Stem-and-leaf plots are not ideal for all situations in particular they are not practical when the data is too tightly clustered. They make it easy to determine the median and mode.They can be used as the data is being collected.They show how data is distributed, and whether it is symmetric around the center. Stem-and-leaf plots have a number of advantages over simply listing the data in a single line. The next two numbers have a common stem of 3. It is the only number with a stem of 2, so that makes it the only number in the 20’s. A stem-and-leaf plot consists of a vertical “stem” containing the first digit of each number, with the rest of each number written to the right of the stem like a “leaf.” In the stem and leaf plot below, the first number represented is 21. Stem-and-leaf plots are especially useful because they give a visual representation of how the data is clustered, but preserve all of the numerical information. \)Īnother useful way to display data is with a stem-and-leaf plot.
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