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Exploratory Data Analysis

We have techniques used to summarize data quickly.

One such technique is the stem-and-leaf display.

Data: 21, 24, 24, 26, 27, 27, 30, 32, 38, 41

2 144677

3 028

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Stem-and-Leaf Display

Each digit on a stem is a leaf.

Each line in the display is referred to as a stem.

To the right of the vertical line we record the next digit for each item in rank order--when the leaf unit is not shown, it is assumed to equal 1.

The first digits of each data item are arranged to the left of a vertical line.

It is similar to a histogram on its side, but it has the advantage of showing the actual data values.

A stem-and-leaf display shows both the rank order and shape of the distribution of the data.

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Example: Hudson Auto Repair

The manager of Hudson Autowould like to have a betterunderstanding of the costof parts used in the enginetune-ups performed in theshop. She examines 50customer invoices for tune-ups. The costs of

parts,rounded to the nearest dollar, are listed on

the nextslide.

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Example: Hudson Auto Repair

Sample of Parts Cost for 50 Tune-ups

91 78 93 57 75 52 99 80 97 6271 69 72 89 66 75 79 75 72 76104 74 62 68 97 105 77 65 80 10985 97 88 68 83 68 71 69 67 7462 82 98 101 79 105 79 69 62 73

First step is to rearrange these data in rank order. See next slide.

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Solution: Stem-and-Leaf Display

56789

10

2 7 2 2 2 2 5 6 7 8 8 8 9 9 9

1 1 2 2 3 4 4 5 5 5 6 7 8 9 9 9 0 0 2 3 5 8 9 1 3 7 7 7 8 9 1 4 5 5 9

a stema leaf

•When the leaf unit is not shown, it is assumed to equal 1.

So What?Explain!

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Solution: Hudson Auto Repair

52 57 62 62 62 62 65 66 67 68 68 68 69 69 69 71 71 72 72 73 74 74 75 75 75 76 77 78 79 79 79 80 80 82 83 85 88 89 91 93 97 97 97 98 99 101 104 105 105 109

Sample of Parts Cost for 50 Tune-ups

Data are rearranged in rank order.

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Tabular and Graphical Procedures

Qualitative DataQualitative Data Quantitative DataQuantitative Data

TabularMethods TabularMethods

TabularMethods TabularMethods

Graphical MethodsGraphical Methods

Graphical MethodsGraphical Methods

• Frequency Distribution• Rel. Freq. Dist.• Percent Freq. Distribution

• Bar Graph• Pie Chart

• Frequency Distribution• Rel. Freq. Dist.• Cum. Freq. Dist.• Cum. Rel. Freq. Distribution • Stem-and-Leaf Display• Crosstabulation (Contingency Table)

• Dot Plot• Histogram• Scatter Diagram

DataData