Statistics Mr. zboril | Milford PEP

Statistics Mr. zboril | Milford PEP
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Chapter 2 Section 2.3 Stem-and-Leaf Displays
You are important to me – don’t ever think otherwise!

Homework Issues Do your homework! Section 2.1 homework was worth 32 points. Several of you either didn’t complete it or ignored the assignment. Class widths are whole numbers, not decimals. When calculating class width, round up to the next whole number even if your calculated result is a whole number. Read and take notes on the next Section that will be covered. Take-Home Test Tuesday 9/19 – due Thurs. 9/21.

Homework Issues After Chapter 3, homework will simply be instructions to complete specific problem numbers on specific pages. These will be in the form of a Weekly Lesson Plan posted on Weebly. There will no longer be an assignment worksheet provided. Do your homework. Take-Home Test Tuesday 9/19 – due Thurs. 9/21.

Section 2.3 Exploratory Data Analysis
Exploratory Data Analysis techniques are useful for detecting patterns and extreme data values. They are designed to help us explore a set of data and to ask questions we had not thought of before. Histograms are one way to analyze and study data in a field known as Exploratory Data Analysis or EDA. Stem-and-Leaf displays are another way to study data.

Section 2.3 Stem-and-Leaf Displays
Section 2.3 will cover stem-and-leaf displays – a method of exploratory data analysis that is used to rank-order and arrange data into groups. Histograms are helpful, but most of the specific data values are lost. Stem-and-leaf displays serve to organize and group data, but also allows us to recover the original data if needed.

Section 2.3 Histogram Review
Example 2 Page 44

Example 6 Stem-and-Leaf Display page 64 Many airline passengers seem weighted down by carry-on luggage. Just how much weight are they carrying? The following is a sample of carry-on weights for 40 passengers returning from a vacation in Hawaii. (We can assume many of the passengers were bringing back goats, silverflowers, and pineapples.) Table Weights of Carry-On Luggage in Pounds 30 27 12 42 35 47 38 36 22 17 29 3 21 32 41 33 26 45 18 43 31 19 28 51

Table Weights of Carry-On Luggage in Pounds 30 27 12 42 35 47 38 36 22 17 29 3 21 32 41 33 26 45 18 43 31 19 28 51 To make a stem-and-leaf display, we break the digits of each value into two parts. (See top of page 65). The left group of digits is called a stem. The right group of digits is called a leaf. The stem may consist of more than one digit. Here, since our values mostly consist of two digits, the stem will be one digit.

Table Weights of Carry-On Luggage in Pounds 30 27 12 42 35 47 38 36 22 17 29 3 21 32 41 33 26 45 18 43 31 19 28 51 Stem-and-Leaf Display (a) Leaves not Ordered 3 2 represents 32 lb Stem Leaves 3 0 1 2 4 5

Stem-and-Leaf Display (b) Leaves Ordered 3 2 represents 32 lb Stem Leaves 0 3 1 2 4 5 There are no firm rules for selecting the group of digits for the stem. Be sure to list all the possible stems from smallest to largest in the data collection.

Section 2.3 Stem-and-Data Procedure
How to Make a Stem-and-Leaf Display Divide the digits of each data value into two parts. The leftmost part is called the stem and the rightmost part is called the leaf. Align the stems in a vertical column from smallest to largest. Draw a vertical line to the right of all the stems. Place all the leaves with the same stem in the same row as the stem, and arrange the leaves in increasing order. Exploratory Data Analysis techniques are useful for detecting patterns and extreme data values. They are designed to help us explore a set of data and to ask questions we had not thought of before.

Guided Exercise 4 Basketball Stem-and-Leaf Display What does it take to win at basketball? One sportswriter listed the winning scores of the conference championship games over the last 35 years. The scores are listed below: Guided Exercise 4 Basketball Stem-and-Leaf Displays 132 118 124 109 104 101 125 83 99 131 98 97 106 112 92 120 103 11 117 135 143 116 119 110 105 128 126 102

Guided Exercise 4 Basketball Stem-and-Leaf Displays 132 118 124 109 104 101 125 83 99 131 98 97 106 112 92 120 103 111 117 135 143 116 119 110 105 128 126 102 To make a stem-and-leaf display, we use the first two digits as the stems. Notice that the distribution of the scores is fairly symmetrical. Use the first two digits as the stem. Provide a label that shows the meaning and units of the first stem and first leaf.

Stem-and-Leaf Display Leaves Ordered 08 3 represents 083 or 83 points 3 09 10 11 12 13 14 Looking at the distributions, would you say that it is fairly symmetrical?

Section 2.3 Stem-and-Leaf Diagrams
Questions?

You are mildly important to me – don’t ever think otherwise!
Chapter 2 Review You are mildly important to me – don’t ever think otherwise!

Homework Issues Do your homework! Section 2.1 homework was worth 32 points. Several of you either didn’t complete it or ignored the assignment. Class widths are whole numbers, not decimals. When calculating class width, round up to the next whole number even if your calculated result is a whole number. Read and take notes on the next Section that will be covered. Take-Home Test Tuesday 9/19 – due Thurs. 9/21.

Chapter 2 Review A frequency table partitions data into classes or intervals and shows how many data values are in each class. Fill-in-the blank – know the chapter definitions. class limits Pareto display time-series chart circle graph outlier cumulative frequency Which graph would be most useful? (pg. 59)

Chapter 2 Review – Circle Graphs and Pie Charts
Create circle graph that contains degrees and percentages. (pg. 57) Guided Exercise 3 on Page 57. How Much Time Do We Spend Talking on the Phone After-Hours? Time Number Fractional Part Percentage Number of Degrees < ½ hour 296 296 / 500 59.2 59.2% x 360o ≈ 213o ½ hour – 1 hour 83 83 / 500 16.6 16.6% x 360o ≈ 60o > 1 hour 121 ----- Total

Section 2.2 Pie Chart or Circle Graphs
Guided Exercise 3 on Page 57. How Much Time Do We Spend Talking on the Phone After-Hours? Time Number Fractional Part Percentage Number of Degrees < ½ hour 296 296 / 500 59.2 59.2% x 360o ≈ 213o ½ hour – 1 hour 83 83 / 500 16.6 16.6% x 360o ≈ 60o > 1 hour 121 121 / 500 24.2 24.2% x 360o ≈ 87o Total 500 500 / 500 100.0 360o

Chapter 2 Review Calculate the class width.
Example 1 on Page 40. Table 2-1 One-Way Commuting Distances for 60 workers in Dallas Texas. (Largest Data Value – Smallest Data Value) / Desired Class Width (47 – 1) ÷ 6 = 7.7 (round up to 8)

Chapter 2 Review Create a stem-and-leaf chart. You don’t need to label ‘Stem’ or ‘Leaves’ but uoi do need to insert a guide (e.g 3 l 2 = 32 lbs) Categorize basic distribution shapes. Understand ogive and be able to draw one. Create a frequency table and relative frequency table.