2. STEM -AND-LEAF DIAGRAMS PRESENTED BY F.6C ESTHER CHAN(2), MAGGIE CHUNG(7), ANITA WAH(23), JODY YU(31) 1-3-2000

3. First of all, let us focus on the stem-and-leaf diagram In recent years a technique known as the stem- and-leaf diagram ( or stemplot ) has become very popular. The technique involves a combination of a graphic technique and a sorting technique. By sorting it means listing the data in rank order according to numerical value. The data values themselves are used to do this sorting. The “stem” is the leading digit(s) of the data, while the “leaf” is the trailing digit.

4. For example, the numerical data 386 might split 38-6 as shown : Leading digits Trailing digit 38 6 ( used in sorting ) (Shown in display ) A stem-and-leaf diagram is a method of presenting a data set so that gaps or concentration in the clarify the process of constructing a stem-and-leaf display.

5. Consider the following set of 30 test scores : 71 85 62 75 78 86 90 53 68 79 69 59 65 76 54 81 70 56 75 80 63 92 68 73 52 80 60 57 74 82 using the first digit as the stem and the second digit as the leaf, we have the following display.

6. 30 Test Score 5 3 9 4 6 2 7 6 3 8 9 5 3 8 0 7 1 5 8 9 6 0 5 3 4 8 5 6 1 0 0 2 9 0 2 In the above display all scores with the same tens digit are placed on the same branch. This may not always be desired. We may reconstruct the diagram so that only five possible values could fall on each stem ( ie.we split each stem in two, one with leaves 0 through 4 and the other with leaves 5 to arrange 9). Moreover, it is a usual practice to arrange the leaves in order of magnitude

7. 5 2 3 4 5 6 7 9 6 0 3 3 6 5 8 8 9 7 0 1 3 4 7 5 5 6 8 9 8 0 0 1 2 8 5 6. 9 0 2 30 Test Score

8. In general, stems may have as many digits as needed, but each leaf should contain only a single digit. Stem -and - leaf displays are well-suited for computer appreciation. Once the data has been entered into the computer, reworking it to create a display with different stems id usually very easy to accomplish.

9. Now, let us talk about the: A dvantages of stem-and -leaf plot: §Easy to construct §Permit the viewer to reconstruct the data set §Easy to identify the order observations D isadvantages of stem - and -leaf plot: §Only suitable for describing small set of data §Little flexibility in the choice of stem §Does not convey a rapid reading of class frequency

10. Example 1 ): The percentage of skill in a material used to manufacture women’s shirt are listed below : 25.8 14.8 20.5 16.8 15.1 18.7 21.3 19.5 16.8 23.4 18.1 23.4 15.5 19.5 24.6 25.3 16.2 17.4 15.6 23.6 22.8 22.5 11.2 12.1 14.1 12.7 24.2 13.6 27.8 22.1 25.8 14.8 20.5 16.8 15.1 18.7 21.3 22.1 11.7 24.5 Construct a stem-and -leaf plot. Hence, find the median of the distribution.

11. Solution Shown below is the resulting stem -and -leaf plot. Stem 11 12 13 14 15 16 17 18 19 20 21 22 23 24 Leaf 27 17 6 188 1156 2888 4 177 55 55 33 1158 446 256 Stem 25 26 27 Leaf 388 0 8

12. Now, let us discus another example- E xample 2) A noise was used to detect the noise level ( in decibel ) during a concert in the Hong Kong stadium. The results are recorded below : 82 74 88 66 58 74 78 84 96 76 62 68 72 92 86 76 52 76 82 78

14. (a) copy and complete the following stem -and -leaf diagram for the above data : Stem ( in 10 decibels) Leaf ( in 1 decibel ) 5 2, 8 6 2, 6, 8 7 2, 4, 4, 6, 8, 8 8 2, 2, 4, 6, 8 9 2, 6

15. (b) Find the median and the interquartile range of the data. Median = 76 decibels Interquartile range = median of upper half - median of lower half = decibels = 13 decibrls