![]() The number 5 is the frequency of the group labeled “80s.” Since there are 30 students in the entire statistics class, the proportion who scored in the 80s is 5/30. In our example of the exam scores in a statistics class, five students scored in the 80s. We will not discuss the process of constructing a histogram from data since in actual practice it is done automatically with statistical software or even handheld calculators. The general purpose of a frequency histogram is very much the same as that of a stem and leaf diagram, to provide a graphical display that gives a sense of data distribution across the range of values that appear. In general, the definition of the classes in the frequency histogram is flexible. ![]() The similarity in Figure 2.1 "Stem and Leaf Diagram" and Figure 2.3 "Frequency Histogram" is apparent, particularly if you imagine turning the stem and leaf diagram on its side by rotating it a quarter turn counterclockwise. The resulting display is a frequency histogram for the data. These classes are arranged and indicated in order on the horizontal axis (called the x-axis), and for each group a vertical bar, whose length is the number of observations in that group, is drawn. Observations are grouped into several classes and the frequency (the number of observations) of each class is noted. The same procedure can be applied to any collection of numerical data. of the class, hence the name frequency histogram. This number is called the frequency Of a class of measurements, the number of measurements in the data set that are in the class. While the individual data values are lost, we know the number in each class. In our example, the bar labeled 100 is 2 units long, the bar labeled 90 is 7 units long, and so on. We then construct the diagram shown in Figure 2.3 "Frequency Histogram" by drawing for each group, or class, a vertical bar whose length is the number of observations in that group. Thus there are two 100s, seven scores in the 90s, six in the 80s, and so on. For the 30 scores on the exam, it is natural to group the scores on the standard ten-point scale, and count the number of scores in each group. We will illustrate it using the same data set from the previous subsection. A frequency histogram A graphical device showing how data are distributed across the range of their values by collecting them into classes and indicating the number of measurements in each class. The stem and leaf diagram is not practical for large data sets, so we need a different, purely graphical way to represent data. There are two perfect scores three students made scores under 60 most students scored in the 70s, 80s and 90s and the overall average is probably in the high 70s or low 80s. Either way, with the data reorganized certain information of interest becomes apparent immediately. The display is made even more useful for some purposes by rearranging the leaves in numerical order, as shown in Figure 2.2 "Ordered Stem and Leaf Diagram". Thus the three leaves 9, 8, and 9 in the row headed with the stem 6 correspond to the three exam scores in the 60s, 69 (in the first row of data), 68 (in the third row), and 69 (also in the third row). The number in the units place in each measurement is a “leaf,” and is placed in a row to the right of the corresponding stem, the number in the tens place of that measurement. The numbers in the tens place, from 2 through 9, and additionally the number 10, are the “stems,” and are arranged in numerical order from top to bottom to the left of a vertical line. One way to do so is to construct a stem and leaf diagram as shown in Figure 2.1 "Stem and Leaf Diagram". However the data set may be reorganized and rewritten to make relevant information more visible. How did the class do on the test? A quick glance at the set of 30 numbers does not immediately give a clear answer.
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