MATH 1580 Oakland Community College Statistics Questions

Class 3
Ch 3.4
Ch 2.3
Organizing
Data
2
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Section
2.3
Stem-and-Leaf
Displays
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Stem-and-Leaf Display
In this text, we will introduce the EDA techniques:
stem-and-leaf displays.
We know that frequency distributions and histograms provide
a useful organization and summary of data. However, in a
histogram, we lose most of the specific data values.
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Stem-and-Leaf Display
A stem-and-leaf display is a device that organizes and
groups data but allows us to recover the original data if
desired.
In the next example, we will make a stem-and-leaf display.
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Example 6 – Stem-and-Leaf Display
Many airline passengers seem weighted down by their
carry-on luggage. Just how much weight are they carrying?
The carry-on luggage weights in pounds for a random
sample of 40 passengers returning from a vacation to
Hawaii were recorded (see Table 2-15).
Weights of Carry-On Luggage in
Pounds
Table 2-15
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Example 6 – Stem-and-Leaf Display cont’d
To make a stem-and-leaf display, we break the digits of
each data value into two parts.
The left group of digits is called a stem, and the remaining
group of digits on the right is called a leaf.
We are free to choose the number of digits to be included
in the stem.
The weights in our example consist of two-digit numbers.
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Example 6 – Stem-and-Leaf Display cont’d
For a two-digit number, the stem selection is obviously the
left digit.
In our case, the tens digits will form the stems, and the
units digits will form the leaves.
For example, for the weight 12, the stem is 1 and the leaf
is 2.
For the weight 18, the stem is again 1, but the leaf is 8.
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Example 6 – Stem-and-Leaf Display cont’d
In the stem-and-leaf display, we list each possible stem
once on the left and all its leaves in the same row on the
right, as in Figure 2-15(a).
(a) Leaves Not
(b) Final Display with Leaves
Ordered
Ordered
Stem-and-Leaf Displays of Airline Carry-On Luggage
Weights
Figure 215
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Example 6 – Stem-and-Leaf Display cont’d
Finally, we order the leaves as shown in Figure 2-15(b).
Figure 2-15 shows a stem-and-leaf display for the weights
of carry-on luggage.
From the stem-and-leaf display in Figure 2-15, we see that
two bags weighed 27 lb, one weighed 3 lb, one weighed
51 lb, and so on.
We see that most of the weights were in the 30-lb range,
only two were less than 10 lb, and six were over 40 lb.
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Example 6 – Stem-and-Leaf Display cont’d
Note that the lengths of the lines containing the leaves give
the visual impression that a sideways histogram would
present.
As a final step, we need to indicate the scale. This is
usually done by indicating the value represented by the
stem and one leaf.
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Stem-and-Leaf Display
Procedure:
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u
Math 1580 HW Two
1.
Colors of Automobiles The popular car colors are shown. These are the
percent for each category. Construct a pie graph for the data
White
Silver
Black
Red
Blue
Gray
Other
19
18
16
13
12
12
10
Source: Dupont Au101,wtive Color Popularity Repon.
2.
Roller Coaster Manla The World Roller Coaster Cen- us Repon lists the
following numbers of roller coasters on each continent. Represent the data
graphically, using a Pareto chart.
Africa
Asia
Australia
Europe
North America
South America
17
315
22
413
643
45
Source: www.rcdb.com
Compare and contrast Histograms, Bar Graphs and Pareto Charts.
4. Dollars for ads Online is shown. (The numbers for 2016 through 2019 are
projected numbers.) Draw a time series graph and comment on the trend.
3.
Year
2014
Amount $19.72
2015
$31.53
2016
$43.83
2017
$53.29
2018
$61.14
2019
$69.04