Brase_Understanding_BasicStats_9e_Section2.3.pptx

understanding basic stats

1. Understanding Basic Statistics , 9e Chapter 2: Organizing Data Brase , Brase , Dolor, Seibert, Understanding Basic Statistics, 9 th Edition. © 2024 Cengage. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

2. 2.3 Stem-and-Leaf Displays

3. Section Objectives By the end of this section, you should be able to: Construct a stem-and-leaf display from raw data. Visualize a data distribution using a stem-and-leaf display. Compare a stem-and-leaf display to a histogram.

4. Stem-and-Leaf Display A stem-and-leaf display is a method of exploratory data analysis that is used to rank order and arrange data into groups.

5. How to Make a Stem-and-Leaf Display (1 of 2) 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 all the stems in a vertical column from smallest to largest. Draw a vertical line to the right of all the stems.

6. How to Make a Stem-and-Leaf Display (2 of 2) 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 include the decimal position in the label rather than with the stems or leaves.

7. Example 6 (1 of 2) Many airline passengers seem weighed 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).

8. Example 6 (2 of 2) Table 2-15: Weights of Carry-On Luggage in Pounds 30 27 12 42 35 47 38 36 27 22 17 29 3 21 38 32 41 26 45 18 43 18 32 31 32 19 33 31 28 29 51 12 32 18 21

9. Example 6: Solution (1 of 4) 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. For a two-digit number, 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. 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 2-26(a). Finally, we order the leaves as shown in Figure 2-26(b).

10. Example 6: Solution (2 of 4) Figure 2-26 Stem-and-Leaf Displays of Airline Carry-On Luggage Weights

11. Example 6: Solution (3 of 4) Figure 2-26 shows a stem-and-leaf display for the weights of carry-on luggage. From the stem-and-leaf display in Figure 2-26, we see that two bags weighed 27 lb., one weighed 3 lbs., 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 lbs., and six were over 40 lbs. Note that the lengths of the lines containing the leaves give the visual impression of a sideways histogram. As a final step, we need to indicate the scale. This is usually done by indicating the value represented by a stem and one leaf.

12. Example 6: Solution (4 of 4) There are no firm rules for selecting the group of digits for the stem. But whichever group you select, you must list all the possible stems from smallest to largest in the data collection.

13. Guided Exercise 4 (1 of 3) What does it take to win at sports? If you’re talking about basketball, one sportswriter gave the answer. He listed the winning scores of the conference championship games over the last 35 years. The scores for those games follow. 132 118 124 109 104 101 125 83 99 131 98 125 97 106 112 92 120 103 111 117 135 143 112 112 116 106 117 119 110 105 128 112 126 105 102

14. Guided Exercise 4 (2 of 3) To make a stem-and-leaf display, we will use the first two digits as the stems (see Figure 2-27) since it would not be feasible to use a single-digit stem to represent values in the data set above 99.

15. Guided Exercise 4 (3 of 3) After aligning all the stems in a vertical column from least to greatest using the first two digits, we then arrange the leaves in the same row as their respective stem in increasing order. We also provide a label that shows the meaning and units of the first stem and leaf. Figure 2-27 shows a label that explains the meaning and units of the first stem and first leaf. b) Interpretation: Based on the stem-and-leaf display, what shape do you think is the distribution of the data? Explain.

16. Guided Exercise 4: Solution (1 of 2) (a) Solution: Figure 2-27: Winning Scores

17. Guided Exercise 4: Solution (2 of 2) (b) Solution: Since stem 11 has the most data and the other data values are equally distributed above and below the stem of 11, then the graph is fairly symmetric .

18. What Do Stem-and-Leaf Display Tell Us? Stem-and-leaf displays give a visual display that Shows us all the data (or truncated data) in order from smallest to largest; Helps us spot extreme data values or clusters of data values; Displays the shape of the data distribution.

19. Critical Thinking Activity (1 of 4) Stem-and-leaf displays show each of the original or truncated data values. We also know that they can be used to understand the shape of the distribution of the data by turning the stem-and-leaf display “sideways.” Furthermore, if there are large gaps between stems containing leaves, especially at the top or bottom of the display, the data values in the first or last lines may be outliers. Consider the stem-and-leaf displays (Figure 2-29) below showing grades from an introductory statistics class. The one on the left presents the data with gaps and the one on the right presents the data without the gaps.

20. Critical Thinking Activity (2 of 4) Figure 2-29

21. Critical Thinking Activity (3 of 4) Consider the following questions: Which of the two images accurately displays the results of the class grades? Why do you think it is necessary for a stem-and-leaf display to show gaps in the stems when displaying the class grades? What is the appropriate shape for the distribution of the class grades?

22. Critical Thinking Activity (4 of 4) Based on the stem-and-leaf display, do you think there might be an outlier in the grades? If so, what do you think is the reason for the outlier? Outliers should be examined carefully to see if they are data errors or simply unusual data values. Someone very familiar with the field of study as well as the purpose of the study should decide how to treat outliers.

23. Summary Click the link to review objectives for this presentation. Link to Objectives