Overview:
In order to use raw data effectively, it must usually be organized in some way. A group of test scores would not be useful unless there was some way to tell how many scores there were, and if any score occurred more frequently than others. One of the shorthand ways to show values is to organize the data in a frequency distribution and then construct a stem-and-leaf-plot from the frequency distribution.
What Is a Frequency Distribution?
A frequency distribution is an arrangement of raw data in such a way to show how many are in each group or within a range. Suppose an experimenter has measured the heights of 20 12 year olds and gets the following values in inches: 64 48 55 68 72 59 57 61 63 60 60 43 67 70 65 55 56 64 61 60. It’s a small group of data, so it is easy to arrange from smallest to largest, and notice that there are some heights that occur more than once: 43 48 55 55 56 57 59 60 60 60 61 61 63 64 64 65 67 68 70 72.
How Can Data Be Grouped?
One of the simplest ways to group this data set is to divide it into four ranges, from 41-49, 50-59, 60-69, and 70-79. In the 41-49 group, there are two scores, 43 48. In the 50-59 group there are five scores, 55 55 56 57 59. In the 60-69 group there are 11 scores, 60 60 60 61 61 63 64 64 65 67 68. In the 70-79 group, there are two scores, 70 72.
How Can Data Be Represented?
The data can be represented in several different ways, in a table, a bar graph, a line graph, or a circle graph. However, a bar graph may lose the exact values. It does show that most 12 year olds in this particular group have heights in the 60-69 inch range.
What Is a Stem and Leaf Plot?
A stem and leaf plot is another way to represent the same data, but without losing any of the raw data. That way, one can see the exact values of the data. The ranges are represented, but so are the exact values. In the stem and leaf plot, the tens place of the raw scores forms the stem and the ones place of the raw scores forms the leaves. A chart can be made with the data as follows:
Stem Leaf
4 3 8
5 5 5 6 7 9
6 0 0 0 1 1 3 4 4 5 7 8
7 0 2
The chart could be then read easily, as the lowest scores are 43 and 48, followed by 55 55 56 57 59, then 60 60 60 61 61 63 64 64 65 67 68, then 70 and 72.
Interested in statistics tutoring services? Learn more about how we are assisting thousands of students each academic year.
SchoolTutoring Academy is the premier educational services company for K-12 and college students. We offer tutoring programs for students in K-12, AP classes, and college. To learn more about how we help parents and students in Augusta, ME visit: Tutoring in Augusta, ME