ch. 2b narrated power points

Chapter Two (Part B): 

Chapter Two (Part B) Descriptive Statistics: Tabular & Graphical Presentations (cont.)

Slide 2: 

Chapter 2 Descriptive Statistics: Tabular and Graphical Presentations Part B Exploratory Data Analysis Cross tabulations and Scatter Diagrams x y

2.3 Exploratory Data Analysis: 

2.3 Exploratory Data Analysis The techniques of exploratory data analysis consist of simple arithmetic and easy-to-draw pictures that can be used to summarize data quickly. One such technique is the stem-and-leaf display . (This is just more ways to present data)

Stem-and-Leaf Display: 

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 last digit for each item in rank order. 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 instead of just bars. A stem-and-leaf display shows both the rank order and shape of the distribution of the data.

Slide 5: 

Example: Hudson Auto Repair The manager of Hudson Auto would like to have a better understanding of the cost of parts used in the engine tune-ups performed in the shop. She examines 50 customer invoices for tune-ups. The costs of parts, rounded to the nearest dollar, are listed on the next slide.

Slide 6: 

Example: Hudson Auto Repair Sample of Parts Cost for 50 Tune-ups REM: this is our data set. Start by finding the lowest number in our data set. It’s 52; so, our stem will start with “5”. The largest number in our data set is 109, so our stem will end with “10”.

Slide 7: 

Stem-and-Leaf Display 5 6 7 8 9 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 stem a leaf As you go through the data set, record the “ones” digit for each observation to the right of the stem. We call the “ones” values “a leaf”.

Stretched Stem-and-Leaf Display: 

Stretched Stem-and-Leaf Display Whenever a stem value is stated twice, the first value corresponds to leaf values of 0 - 4, and the second value corresponds to leaf values of 5 - 9. That is, we want each stem to be like a class, i.e. of equal value or amount. If we believe the original stem-and-leaf display has condensed the data too much, we can stretch the display by using two stems for each leading digit(s). Why are we doing this? Easier to construct by hand Shows the actual data, although it takes some interpreting

Slide 9: 

Stretched Stem-and-Leaf Display 5 5 9 1 4 7 7 7 8 9 1 3 5 8 9 0 0 2 3 5 5 5 6 7 8 9 9 9 1 1 2 2 3 4 4 5 6 7 8 8 8 9 9 9 2 2 2 2 7 2 5 5 6 6 7 7 8 8 9 9 10 10

Slide 10: 

Stem-and-Leaf Display Leaf Units Where the leaf unit is not shown, it is assumed to equal 1. Leaf units may be 100, 10, 1, 0.1, and so on. In the preceding example, the leaf unit was 1. A single digit is used to define each leaf. Why?? Example in book : it uses a leaf value of 10 and does not round the data variables up or down; therefore, the leafs are approximate. We can do it another way, where the leaf unit = 0.1 ….

Example: Leaf Unit = 0.1: 

Example: Leaf Unit = 0.1 If we have data with values such as 8 9 10 11 Leaf Unit = 0.1 6 8 1 4 2 0 7 8.6 11.7 9.4 9.1 10.2 11.0 8.8 a stem-and-leaf display of these data will be

Slide 12: 

Example: Leaf Unit = 10 If we have data with values such as 16 17 18 19 Leaf Unit = 10 8 1 9 0 3 1 7 1806 1717 1974 1791 1682 1910 1838 a stem-and-leaf display of these data will be The 82 in 1682 is written as an 8. The leafs are not rounded.

Paulsen’s Preferred Stem & Leaf: 

Paulsen’s Preferred Stem & Leaf 1806 1717 1974 1791 1682 1910 1838 16 17 18 19 82 91 06 38 10 74 Why? Because stem & leaf displays are supposed to show you the data values in addition to the shape of the distribution. If you round or cut off digits, you are not showing the actual data values and the system loses part of its value.

Summary: Tabular and Graphical Procedures: 

Summary: Tabular and Graphical Procedures Categorical Data Quantitative Data Tabular Methods Tabular Methods Graphical Methods Graphical 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 Dot Plot Histogram Ogive Data This is Fig. 2.9 in text.

End of Chapter 2, Part B: 

End of Chapter 2, Part B