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| Math
A |
Stem-and-Leaf
Plots |
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Data
can be displayed in many ways. One method of displaying a
set of data is with a stem-and-leaf plot.
A
stem-and-leaf plot is a display that organizes data to show its
shape and distribution. |
In a stem-and-leaf plot each data value
is split into a "stem" and a "leaf".
The "leaf" is usually the last digit
of the number and the other digits to the left of the "leaf" form the "stem".
The number 123 would be split as:
Constructing
a stem-and-leaf plot:
The data:
Math test scores out of 50 points: 35, 36, 38, 40, 42, 42, 44, 45,
45, 47, 48, 49, 50, 50, 50.
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Writing the data in numerical
order may help to organize the data, but is NOT a required step.
Ordering can be done later.
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35, 36, 38, 40, 42, 42, 44, 45,
45, 47, 48, 49, 50, 50, 50 |
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Separate each number into a stem and a
leaf. Since these are two digit numbers, the tens digit is the stem
and the units digit is the leaf. |
The number 38 would be represented as
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Group the numbers with the same
stems. List the stems in numerical order. (If your leaf values
are not in increasing order, order them now.) Title the graph. |
Math Test Scores
(out of 50 pts) |
| Stem |
Leaf |
| 3 |
5 6 8 |
| 4 |
0 2 2 4 5 5 7 8 9 |
| 5 |
0 0 0 |
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Prepare an appropriate legend
(key) for the graph. |
Legend: 3 | 6 means 36 |
A stem-and-leaf plot shows the shape and distribution of
data. It can be clearly seen in the diagram above that the data clusters
around the row with a stem of 4.
Notes:
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The leaf
is the digit in the place farthest to the right in the number, and the
stem is the digit, or digits, in the
number that remain when the leaf is dropped.
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To show a one-digit number
(such as 9) using a stem-and-leaf plot,
use a stem of 0 and a leaf of 9.
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To find the median in a stem-and-leaf plot, count off
half the total number of leaves.
Special
Case:
If you are comparing two sets of data,
you can use a back-to-back
stem-and-leaf plot.
| Data
Set A |
|
Data
Set B |
| Leaf |
Stem |
Leaf |
|
3 2 0 |
4 |
1 5 6 7 |
The numbers 40, 42, and 43 are from Data Set A.
The numbers 41, 45, 46, and 47 are from Data Set B.
Are Stem-and-Leaf
Plots "tipped over" Histograms?
A stem-and-leaf plot does resemble a histogram
turned sideways. The stem values could represent the intervals of a
histogram, and the leaf values could represent the frequency for each
interval.
One advantage to the stem-and-leaf plot over
the histogram is that the stem-and-leaf plot displays not only the frequency
for each interval, but also displays all of the individual values within that
interval.
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