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12-1 Stem-and-Leaf Plots

12-1 Stem-and-Leaf Plots. How can stem-and leaf plots help you understand an election?. Please read with your group.

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12-1 Stem-and-Leaf Plots

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  1. 12-1 Stem-and-Leaf Plots How can stem-and leaf plots help you understand an election?

  2. Please read with your group. The members of the Electoral College officially elect the President of the United States. These members are called electors. The number of electors for each state, including the District of Columbia, is shown (Source: The World Almanac):

  3. Now, with your group, please write each number on individual pieces of scrap paper.

  4. Group the numbers: 0-9, 10-19, 20-29, 30-39, 40-49, and 50-59. • Organize the numbers in each group from least to greatest. • Please discuss the following questions with your group, and write your answers on the guide: • Is there an equal number of electors in each group? Explain. • Name an advantage of displaying the data in groups.

  5. Now, it’s time to take notes… please copy the following slide.

  6. Display Data • One way to organize and display data is through a stem-and-leaf plot. • stem-and-leaf plot – numerical data are listed in ascending or descending order • stems – the greatest place value of the data • leaves – the next greatest place value of the data

  7. Example – Draw a Stem-and-Leaf Plot- Please copy the STEPS – you do not need to copy the actual example. • We will display the data shown as a stem-and-leaf plot. The chart is a record of the top ten oldest US. Astronauts at the time of their last space shuttle flight (Source: Top Ten of Everything, 2001):

  8. Step One – Find the least and greatest number. Then identify the greatest place value digit in each number. In this case, the greatest place value digit is in the tens. 54 74 The greatest number has a 7 in the tens place. The least number has a 5 in the tens place.

  9. Step 2 – Draw a vertical line and write the stems from 5 to 7 on the left of the line. Stem 5 6 7

  10. Step 3 – Write the leaves to the right of the line, with the corresponding stem. For example, for 56, write 6 to the right of 5. Stem 5 6 4 4 4 6 9 4 8 6 1 7 7

  11. Step 4 – Rearrange the leaves so they are ordered from least to greatest. Then include a key or explanation. Stem Stem 5 6 4 4 4 6 9 4 5 4 4 4 4 6 6 8 9 8 6 1 6 1 7 7 7 7 5|6 = 56 years The key tells what the stems and leaves represent.

  12. Now, please complete the problem “Draw a Stem-and-Leaf Plot” on your guide.

  13. Interpret Stem-and-Leaf Plots It is often easer to interpret data when they are displayed in a stem-and-leaf plot instead of a table. You can “see” how the data are distributed.

  14. You do not need to copy the following example, but you will see some questions. Please discuss with your group BEFORE you click to see the answer.

  15. Example – Interpret Data The stem-and-leaf plot lists the ages of the U.S. Presidents at the time of their inauguration (Source: The World Amanac, 2001). 5|0 = 50 years Fun Fact: The first president was George Washington. He was 57 years old at the time of his inauguration. He served as President from 1789 to 1797 and earned $25,000 per year(Source: www.infoplease.com). Source: www.wikipedia.com

  16. In which interval do most of the ages occur? Most of the data occurs in the 50-59 interval. What is the age difference between the youngest and oldest President? The youngest age is 42. The oldest age is 69. The difference between these ages is 69 – 42, or 27. What is the median age of a President at inauguration? The median, or number in the middle, is 55. 5|0 = 50 years

  17. Now, please complete the problem “Interpret Data” on your guide.

  18. Vocabulary – Please copy into your notebook. back-to-back stem-and-leaf plot – a way of comparing two sets of data The back-to-back stem-and-leaf plot below shows the scores of two basketball teams for the games in one season. The leaves for the other set of data are on the other side of the stem. The leaves for one set of data are on one side of the stem.

  19. You do not need to copy the following examples, but you will see some questions. Please discuss with your group BEFORE you click to see the answer.

  20. Example – Compare Two Sets of Data The average monthly temperatures for Helena, Montana and Seattle, Washington are shown (Source: The World Almanac):

  21. Which city has lower monthly temperatures? Explain. Helena; it experiences temperatures in the 20’s and the 30’s. Which city has more varied temperatures? Explain. The data for Helena are spread out from to 20’s to the 60’s. The data for Seattle are clustered from the 40’s to the 60’s. So, Helena has the more varied temperatures.

  22. Now, please complete the problem “Compare Two Sets of Data” on your guide.

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