Solution: The stem‐and‐leaf plot for the data in Table 2.4.5 is as shown in Figure 2.4.13.
The first column in Figure 2.4.13 gives the cumulative frequency starting from the top and from the bottom of the column but ending at the stem that lies before the stem containing the median. The number in parentheses indicates the stem that contains the median value of the data, and the frequency of that stem.
Figure 2.4.13 Stem‐and‐leaf plot for the data in Example 2.4.7 with increment 10.
Figure 2.4.14 Stem‐and‐leaf plot for the data in Example 2.4.7 with increment 5.
Carefully examining the stem‐and‐leaf plot in Figure 2.4.13, we note that the data are clustered together; each stem has many leaves. This situation is the same as when we have too few classes in a frequency distribution table. Thus having too many leaves on the stems makes the stem‐and‐leaf diagram less informative. This problem can be resolved by splitting each stem into two, five, or more stems depending on the size of the data. Figure 2.4.14 shows a stem‐and‐leaf plot when we split each stem into two stems.
The first column in the above stem‐and‐leaf plots counts from the top, and at the bottom is the number of workers who have produced up to and beyond certain number of parts. For example, in Figure 2.4.14, the entry in the third row from the top indicates that 35 workers produced fewer than 75 parts/wk, whereas the entry in the third row from the bottom indicates that 37 workers produced at least 80 parts/wk. The number within parentheses gives the number of observations on that stem and indicates that the middle value or the median of the data falls on that stem. Furthermore, the stem‐and‐leaf plots in Figure 2.4.14 is more informative than Figure 2.4.13. For example, the stem‐and‐leaf plot in Figure 2.4.14 clearly indicates that the data is bimodal, whereas Figure 2.4.13 fails to provide this information. By rotating the stem‐and‐leaf plot counterclockwise through 90°, we see that the plot can serve the same purpose as a histogram, with stems as classes or bins, leaves as class frequencies, and columns of leaves as rectangles or bars. Unlike the frequency distribution table and histogram, the stem‐and‐leaf plot can be used to answer questions such as, “What percentage of workers produced between 75 and 83 parts (inclusive)?” Using the stem‐and‐leaf plot, we readily see that 20 of 80, or 25% of the workers, produced between 75 and 83 parts (inclusive). However, using the frequency distribution table, this question cannot be answered, since the interval 80–85 cannot be broken down to get the number of workers producing between 80 and 83 per week. It is clear that we can easily retrieve the original data from the stem‐and‐leaf plot.
MINITAB
1 Enter the data in column C1.
2 From the Menu bar, select Graph Stem‐and‐leaf. This prompts the following dialog box to appear on the screen. In this dialog box,
3 Enter C1 in the box under Graph variables.
4 Enter the desired increment in the box next to Increment. For example, in Figures 2.4.13 and 2.4.14, we used increments of 10 and 5, respectively.
5 Click OK. The stem‐and‐leaf plot will appear in the Session window.
USING R
We can use the built in ‘stem()’ function in R to generate stem‐and‐leaf plots. The extra argument ‘scale’ can be used to define the length of the stem. The task can be completed by running the following R code in R Console window.
SpareParts = c(73,70,68,79,84,85,77,75,61,69,74,80,83,82,86,87,78,81, 68,71,74,73,69,68,87,85,86,87,89, 90,92,71,93,67,66,65,68,73,72,83, 76,74,89,86,91,92,65,64,62,67,63,69,73,69,71,76,77,84,83,85,81,87, 93,92,81,80,70,63,65,62,69,74,76,83,85,91,89,90,85,82) #To plot stem‐and‐leaf plot stem(SpareParts, scale = 1) #R output
| The decimal point is 1 digit(s) to the right of the | | ||
| 6 | | | 122334 |
| 6 | | | 555677888899999 |
| 7 | | | 00111233334444 |
| 7 | | | 56667789 |
| 8 | | | 0011122333344 |
| 8 | | | 555556667777999 |
