STEM -AND-LEAF DIAGRAMS
PRESENTED BY
F.6CESTHER CHAN(2) , MAGGIE CHUNG(7),
ANITA WAH(23) , JODY YU(31)
1-3-2000
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 .
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.
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 .
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
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
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 .
Now , let us talk about the:
Advantages of stem-and -leaf plot: Easy to construct Permit the viewer to reconstruct the data set Easy to identify the order observations
Disadvantages 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
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 .
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
Now , let us discus another example-
Example 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
(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
(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
2
7268
2
8482
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