14.2 Stem-and-Leaf Plots CORD Math Mrs. Spitz Spring 2007

Objectives  Display and interpet data on a stem-and- leaf plot

Assignment  pp #1-21

Application  Mr Juarez wants to study the distribution of the scores for a 100-point unit exam given in his first period biology class. The scores of the 35 students in the class are listed below

Organizing Data  He can organize and display the scores in a compact way by using a stem-and-leaf plot. In a stem-and-leaf plot, the greatest common place value of the data is used to form the stems. The numbers in the next greatest common place-value position are then used to form the leaves. In the list previously given, the greatest place value is tens. Thus, the number 82 would have stem 8 and leaf 2.

To make a stem-and-leaf plot  First, make a vertical list of the stems. Since the test scores range from 44 to 99, the stems range from 4 to 9. Then, plot each number by placing the units digit (leaf) to the right of its correct stem. Thus, the scores 82 is plotted by placing leaf 2 to the right of the stem 8. The complete stem-and- leaf plot is shown at the right. StemLeaf |2 represents a score of 82. Note: a stem may have one or more digits. A leaf always has just one digit.

To make a stem-and-leaf plot  A second stem-and- leaf plot can be made to arrange the leaves in numerical order from least to greatest as shown at the right. This will make it easier for Mr. Juarez to analyze the data. StemLeaf

Ex. 1: Use the information in the stem-and- leaf plots above to answer each question. 1. What were the highest and the lowest scores? StemLeaf Which test score occurred most frequently? 3. In which 10-point interval did the most students score? 4. How many students received a score of 70 or better? 99 and (3 times) 80-89(10 students) 25 students

More than 2 digits  Sometimes the data for a stem-and-leaf plot are numbers that have more than two digits. Before plotting the numbers, they may need to be rounded or truncated to determine each stem and leaf. Suppose you want to plot 356 using the hundreds digit for the stem.  Rounded: Round 356 to 360. Thus you would plot 356 using stem 3 and leaf 6. What would be the stem-and-leaf of 499? 5 and 0

More than 2 digits  Truncated—To truncate means to cut off, so truncate 356 as 350. Thus you would plot 356 using stem 3 and leaf 5. What would be the stem and leaf of 499? 4 and 9

Back-to-back stem-and-leaf  A back-to-back stem-and-leaf plot is sometimes used to compare two data or rounded and truncated values of the same data set. In a back-to-back plot, the same stem is used for the leaves of both plots.

Ex. 2: The average annual pay for workers in selected states are listed below. Make a back-to-back stem-and-leaf plot of the average annual pay comparing rounded values and truncated values. Then answer each question. StateAvg. Annual Pay StateAvg. Annual Pay Alaska$28,033Michigan$24,193 California$24,126Minnesota$21,481 Colorado$21,472New Jersey$25,748 Connecticut$26,234New York$26,347 Delaware$21,977Ohio$21,501 Illinois$23,608Pennsylvania$21,485 Maryland$22,515Texas$21,130 Massachusetts$24,143Virginia$21,053

Ex. 2: Since the data range from $21,053 to $28,033, the stems range from 21 to 28 for both plots. StateAvg. Annual Pay StateAvg. Annual Pay Alaska$28,033Michigan$24,193 California$24,126Minnesota$21,481 Colorado$21,472New Jersey$25,748 Connecticut$26,234New York$26,347 Delaware$21,977Ohio$21,501 Illinois$23,608Pennsylvania$21,485 Maryland$22,515Texas$21,130 Massachusett s $24,143Virginia$21,053 RoundedStemTruncated

Ex. 2: Since the data range from $21,053 to $28,033, the stems range from 21 to 28 for both plots. a. What does 21|5 represent in each plot? RoundedStemTruncated Answer: It represents $21,450 to $21,549 for rounded data and $21,500 to $21,599 for truncated data.

Ex. 2: Since the data range from $21,053 to $28,033, the stems range from 21 to 28 for both plots. RoundedStemTruncated b. What is the difference between the highest lowest average annual pay? Answer: About $6,900 for rounded data and $7,000 for truncated data.

Ex. 2: Since the data range from $21,053 to $28,033, the stems range from 21 to 28 for both plots. RoundedStemTruncated c. Did more of the states have average annual pay above or below $25,000? Answer: Below $25,000

Ex. 2: Since the data range from $21,053 to $28,033, the stems range from 21 to 28 for both plots. RoundedStemTruncated d. Does there appear to be any significant difference between the two stem-and- leaf plots? Answer: NO

Ex. 3: Set up the problem  The enrollment of several small colleges in the Center City area are listed below. Make a back- to-back stem-and-leaf plot of enrollments comparing rounded values and truncated values. Then answer each question. CollegeEnrollment Figure Miller Business School1342 Capital College1685 Para-Professional Institute1013 Parke College2350 State Community3781 Fashion Institute1096 College of Art and Design1960 Franklin Community College3243

Ex. 3: Since the data range from 1013 to 3781, we an use stems that represent 1,000 each. RoundedStemTruncated a. What range of student enrollment is represented on the rounded side by 2|4? Answer:

Ex. 3: Since the data range from 1013 to 3781, we an use stems that represent 1,000 each. RoundedStemTruncated b. What range of student enrollment is represented on the truncated side by 1|9? Answer: Since each stem represents 1,000; for example 3|8 represents 3,000-3,999