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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