Another representation that is similar to a histogram is the Stamplot . Stemplot is also known as stem-and-leaf plot. In statistics, a stemp plot is a tool for presenting quantitative data in a graphical format, similar to a histogram, which is to assist in visualizing the shape of the distribution of data that is often used in exploratory analysis .
Stemplots were introduced by Arthur Bowley in the early 1900s. However, its general use only began in 1980 after John Tukey's published Exploratory Data Analysis in 1977. Stem-and-leaf plots provide more information about true values than histograms. As in the histogram , the length of each bar corresponds to the number of events that fall into a certain interval. On the Histogram. we can only see the frequency value from the data but we don't know what the actual number value is. Unlike the histogram, on the Stem-and-leaf plotIn addition to knowing the frequency value, we can also know what the actual data value is. This is done by dividing the observed values into two components, stem and leaf .
Stem-and-Leaf Plot
Stem-and-leaf plots describe/present data by separating each value into two parts: the stem ( stem ) which is the leftmost digit number and followed by the next number, namely the leaf ( leaf ), the rightmost digit. The main purposes of a stem-and-leaf plot are the following:
- Is the observation pattern symmetrical.
- The spread or variation of observational data.
- Are there any outliers (outliers, values that are far from each other).
- Data center point.
- There are Locations that are gaps (gaps in the data)
The illustration below shows a Stem-and-leaf plot for 80 students' Test Scores.
79 49 48 74 81 98 87 80
80 84 90 70 91 93 82 78
70 71 92 38 56 81 74 73
68 72 85 51 65 93 83 86
90 35 83 73 74 43 86 88
92 93 76 71 90 72 67 75
80 91 61 72 97 91 88 81
70 74 99 95 80 59 71 77
63 60 83 82 60 67 89 63
76 63 88 70 66 88 79 75
The following is a Stem-and-Leaf Plot generated by MINITAB for the Test Score data above. MINITAB:
Stem-and-leaf of Nilai Ujian N = 80
Leaf Unit = 1.0
2 3 58
5 4 389
8 5 169
19 6 00133356778
(24) 7 000011122233444455667899
37 8 0000111223334566788889
15 9 000111223335789
^ ^ ^
f stem | leaf
If we look at the output of the Minitab software, there are 3 parts, namely f, stem, leaf . The first part is the frequency value (f) which is placed on the far left, followed by the stem (in the middle) and finally the leaf (on the right). The test scores on the stem and leaf plots are sorted in ascending order, starting with the smallest value, 35, 38, 43, 48, …., 97, 98, 99. It is easy to see how the first value, 35 , is separated into two separate sections. , 3 is inserted into the stem, and 5 is put into the leaf. Likewise, test scores of 38 , 3 (stem) and 8 (leaf). Because the numbers 35 and 38 have the same tens digit (i.e. the number 3), then both values are placed on the same stem, and the units are grouped on the same leaf (note the number 58 ). On stem 3 there are only 2 leaves, namely numbers 5 and 8 which means that on stem 3 the frequency is 2. On Minitab, the number 2 can be seen in the row to the left of the stem.
Interpretation:
- The distribution of the data is not symmetrical (normal) but skewed/protrudes to the left
- The mode occurs in the 70s Exam Score, which is as many as 24 pieces which are data center points
- Exam score of 35, 38 may be an outlier
Addendum: Exam Score computer output using SPSS software:
Nilai Ujian Stem-and-Leaf Plot
Frequency Stem & Leaf
3.00 Extremes (=<43)
2.00 4 . 89
3.00 5 . 169
11.00 6 . 00133356778
24.00 7 . 000011122233444455667899
22.00 8 . 0000111223334566788889
15.00 9 . 000111223335789
Stem width: 10
Each leaf: 1 case(s)
How to Create a Stem-and-Leaf-Plot
Example:
Create a stem-and-leaf plot for the following data:
23 26 26 30 32 36 38 43 44 45 48 49 53 57 58 65 66 99
To construct a stem plot, the observational data must first
be sorted in ascending order.
The data above has been sorted in ascending order.
Next, we make the numbers above into two components/sections/columns,
namely stem and leaf.
Tens digits for stems and units digits for leaves.
Then we separate the tens and ones digits
with a "|"
Ok, let's start:
23 26 26 30 32 36 38 43 44 44 45 48 49 53 57 58 65 66 99
Example for the first three numbers, 23 26 and 26
The tens digit is the same, namely 2 so that the number is
placed on the same stem and
the units digit, 3, 6, 6 is placed on the same leaf
so as to form leaf 366 .
If we put it in the form of Stem-and-leaf-plot:
2 | 366
Stem and full leaf plots:
------------------------------------------------- ------------
Stem (tens) | leaf (unit)
---------------------------------------------------- ---------
2 | 366 (value = 23 26 26 )
3 | 0268 (value = 30 32 36 38)
4 | 344589 (value = 43 44 44 45 48 49)
5 | 378 (value = 53 57 58)
6 | 56 (value = 65 66)
7 | (no value)
8 | (no value)
9 | 9 (value = 99)
-------------------------------------------------- -----------
Explanation:
We will separate the first number: 23 into 2 (stem) and 3 (leaf)
2|3
(remarks: Number 2 is tens so that it becomes stem,
and number 3 is unit, so used as a leaf)
The second number: 26 we separate into 2 (stem) and 6 (leaf)
The third number: 26 we separate into 2 (stem) and 6 (leaf)
(remarks: the first three numbers: 23, 26, and 26
have the same stem, which is 2 so that the unit digits
are placed in the same leaf row,
see number 366 (leaf) in the image below)
:
etc.
Interpretation:
- Not symmetrical, data is skewed (sticking) to the right
- Number 99 is an outlier
- Gaps (data gaps / gaps) are in stems: 7 and 8
- Centralization of data occurs on stem 4, around 4 tens.
Reference:
Wild, C. and Seber, G. (2000) Chance Encounters: A First Course in Data Analysis and Inference pp. 49-54 John Wiley and Sons. ISBN 0-471-32936-3
