AP* Statistics: Stemplots (aka, Stem and Leaf Plots)
Although a
histogram
shows how observations are distributed across groups, it does
not show the exact values of individual observations. A
different kind of graphical display, called a
stemplot or a stem and leaf plot,
does show exact values of individual observations.
Stemplots
A stemplot is used to display quantitative data, generally from
small data sets (50 or fewer observations). The stemplot below
shows IQ scores for 30 sixth graders.
Stems
150
140
130
120
110
100
90
80
Key: 110
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Leaves
1
2 6
4 5 7 9
1 2 2 2 5 7 9 9
0 2 3 4 4 5 7 8 9 9
1 1 4 7 8
7 represents an IQ score of 117
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In a stemplot, the entries on the left are called stems; and the entries
on the right are called leaves. In the example above, the stems are
tens (80 and 90) and hundreds (100 through 140). However, they could
be other units - millions, thousands, ones, tenths, etc. In the
example above, the stems and leaves are explicitly labeled for
educational purposes. In the real world, however, stemplots usually do not
include explicit labels for the stems and leaves.
Some stemplots include a key to help the user interpret the display correctly.
The key in the stemplot above indicates that a stem of 110 with a leaf of
7 represents an IQ score of 117.
Looking at the example above, you should be able to quickly describe the
distribution of IQ scores. Most of the scores are clustered between
90 and 109, with the center falling in the neighborhood of 100. The
scores range from a low of 81 (two students have an IQ of 81) to a
high of 151. The high score of 151 might be classified as an
outlier.
Test Your Understanding of This Lesson
Problem 1
The stemplot below shows the number of hot dogs eaten by contestants in
a recent hot dog eating contest.
80
70
60
50
40
30
20
10
|
1
4 7
2 2 6
0 2 5 7 9 9
5 7 9
7 9
1
|
Which of the following statements are true?
I. The range is 70.
II. The median is 46.
(A) I only
(B) II only
(C) I and II
(D) Neither is true.
(E) There is insufficient information to answer this question.
Solution
The correct answer is (C). The
range
is equal to the biggest value minus the smallest value. The
biggest value is 81, and the smallest value is 11; so the
range is equal to 81 -11 or 70.
The
median is equal
to the middle value in the data set. Here, we have an even number
of values - 45 and 47 - in the middle of the data set. Their average
is (45 + 47)/2 or 46, so the median is equal to 46.
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