# 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.

0

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

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