2.3 Stem-and-Leaf Displays CHAPTER 2 ORGANIZING DATA
Exploratory Data Analysis Together with histograms and other graphics techniques, the stem-and-leaf display is one of many useful ways of studying data in a field called exploratory data analysis (often abbreviated as EDA).
Pg. 63 Exploratory Data Analysis Exploratory data analysis techniques are particularly useful for detecting patterns and extreme data values. EDA methods help us quickly absorb some aspects of the data and then may lead us to ask specific questions to which we might apply methods of traditional statistics. EDA methods are especially useful when our data have been gathered for general interest and observation of subjects EDA techniques Stem-and-Leaf Displays Box-and-Whisker Plots (section 3.3)
Pg. 64 Stem-and-Leaf Displays A stem-and-leaf display is a method of exploratory data analysis that is used to rank-order and arrange data into groups. Stem-and-leaf displays retains original data and individual information Stem-and-leaf diagrams provide a very effective way of ordering data by hand By looking at the display “sideways” you can see the distribution shape of the data
Pg. 65 To Make a Stem-and-Leaf Display1. 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. There are no firm rules for selecting the group of digits for the stem. Whichever group you choose, you must list all the possible stems from smallest to largest in the data collection.2. Align all the stems in a vertical column from smallest to largest. Draw a vertical line to the right of all the stems.3. Place all the leaves with the same stem in the same row as the stem, and arrange the leaves in increasing order.4. Use a label to indicate the magnitude of the numbers in the display. We use the decimal position in the label rather than with the stems or leaves. Always include a scale/key!
Example 6 Page 64 Stem-and-Leaf DisplayMany airline passengers seemweighted down by their carry-onluggage. Just how much weight arethey carrying? The carry-on luggageweights in pounds for a randomsample of 40 passengers returningfrom a vacation to Hawaii wererecorded (see Table 2-15). Weights of Carry-On Luggage in Pounds Table 2-15
Page 69 How to Split a Stem When a stem has many leaves, it is useful to split the stem into two lines (or more). For two lines per stem: Place leaves 0 – 4 on the first line Place leaves 5 – 9 on the second line
Page 70 Back-to-Back Stem Plot A back-to-back stem plot is used to compare to sets of data. The stems are in the middle of the diagram with the leaves extending out on both sides
Assignments Homework Page 67 #1, 2, 5, 10 Classwork/Graded Assignment This assignment will be collected and graded. 50 points for completion, 50 points for “correctness”. P72 #1, 4, 6, 9, 10, 11