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Stem-and-Leaf Plot

Stem-and-Leaf Plot. 7 th Pre – Algebra Lesson 11-2. What is a stem-and-leaf plot?. A T-chart that is used to show numeric data and the distribution of numbers. Why would I want to use one?. It displays a lot of numbers in a neater, cleaner, and organized way.

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Stem-and-Leaf Plot

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  1. Stem-and-Leaf Plot 7th Pre – Algebra Lesson 11-2

  2. What is a stem-and-leaf plot? • A T-chart that is used to show numeric data and the distribution of numbers

  3. Why would I want to use one? • It displays a lot of numbers in a neater, cleaner, and organized way. • It makes it easier to see how spread out the numbers are • It is easier to identify outliers

  4. Reading a Stem-and-Leaf Plot(how to analyze and make inferences)

  5. Things you need to know… • Stems • The stems include the digits in the tens place and higher (sometimes the units place too, if data includes decimals) • The top of the stem includes all but the last digits of the smallest number • The bottom of the stem includes all but the last digit of the largest number • Your stems need to include ALL consecutive numbers in between—even if there is no data for it.

  6. Things you need to know… • leaves • The leaves are always from the LAST digit from your data (usually ones place) • The leaves need to be organized from least to greatest • You can have multiples of the same digit per line (interval)

  7. What does it look like? The stem-and-leaf plot below shows the number of students enrolled in a dance class in the past 12 years. The number of students are 81, 84, 85, 86, 93, 94, 97, 100, 102, 103, 110, and 111. 8 | 4 means 84

  8. Should I skip numbers in my stem? You HAVE TO include all of the consecutive numbers from the first stem until the last one. Notice how 6, 7, and 10 have no data next to them. It means that no countries reported sixties, seventies, or one hundreds of infant deaths. You CANNOT put a zero in the leaf spot because that implies that you have data for that stem—which you don’t. No! This chart shows the number of infant deaths per 1,000 live births, of countries in Western Africa.

  9. Making a Stem-and-Leaf Plot

  10. This stem-and-leaf plot shows points that students received on a science quiz. 73 75 76 78 40 49 49 56 58 59 61 64 67 67 67 80 85 87 88 92 96 100 100 4 0 9 9 5 6 8 9 6 1 4 7 7 7 7 3 5 6 8 8 0 5 7 8 9 2 6 10 0 0

  11. Finding the Range, Mode,Median, and Mean

  12. Range= biggest number – smallest number 40 is the smallest number 73 75 76 78 40 49 49 56 58 59 61 64 67 67 67 80 85 87 88 92 96 100 100 4 0 9 9 100 – 40 = 60 The range for this data set is 60 points. 5 6 8 9 6 1 4 7 7 7 7 3 5 6 8 100 is the largest number 8 0 5 7 8 9 2 6 10 0 0 This stem-and-leaf plot shows points that students received on a science quiz.

  13. Finding the Median (the middle number) Start counting with this leaf! 73 75 76 78 40 49 49 56 58 59 61 64 67 67 67 80 85 87 88 92 96 100 100 Leaf number 12… This is the halfway point! 4 0 9 9 I have 23 leaves. If I divided that in half, I would end up with 11.5. This means that the 12th number is my median. 23 ÷ 2 = 11.50  the 12th number will be our median. The twelfth number is 73. This is my median. 5 6 8 9 6 1 4 7 7 7 7 3 5 6 8 8 0 5 7 8 9 2 6 10 0 0 This stem-and-leaf plot shows points that students received on a science quiz.

  14. Finding the Mode (the number that shows up most) You have more 7s than 9s or 0s. That means 67 is your mode. 73 75 76 78 40 49 49 56 58 59 61 64 67 67 67 80 85 87 88 92 96 100 100 4 0 9 9 For the mode, look at each row of leaves separately. If you see more than one of a number, underline it. After looking at all your rows, pick the underlined number that has the most digits. 5 6 8 9 6 1 4 7 7 7 7 3 5 6 8 8 0 5 7 8 9 2 6 10 0 0 This stem-and-leaf plot shows points that students received on a science quiz.

  15. Finding the Mean (the average) 73 75 76 78 40 49 49 56 58 59 61 64 67 67 67 80 85 87 88 92 96 100 100 4 0 9 9 To find the mean, you will be doing a combination of Multiplying, adding, and dividing. 5 6 8 9 6 1 4 7 7 7 7 3 5 6 8 8 0 5 7 8 9 2 6 10 0 0 This stem-and-leaf plot shows points that students received on a science quiz.

  16. Finding the Mean (the average) We will start by adding a zero to the end of the stem and then multiplying that number times the number of leaves you have. 4 0 9 9 5 6 8 9 6 1 4 7 7 7 7 3 5 6 8 8 0 5 7 8 9 2 6 10 0 0 This stem-and-leaf plot shows points that students received on a science quiz.

  17. Finding the Mean (the average) 2 4 0 9 9 4 0 x 3 = 120 5 6 8 9 5 0 x 3 = 150 6 0 x 5 = 300 6 1 4 7 7 7 7 3 5 6 8 7 0 x 4 = 280 8 0 x 4 = 320 8 0 5 7 8 9 0 x 2 = 180 9 2 6 10 0 0 10 0 x 2 = 200 15 5 0

  18. Finding the Mean (the average) Now add up all your leaves. Look around the entire Stem-and-Leaf Plot. Try to make tens or multiples of five. This will make it easier for you to add quickly. 4 0 9 9 4 0 x 3 = 120 5 6 8 9 5 0 x 3 = 150 6 0 x 5 = 300 6 1 4 7 7 7 7 3 5 6 8 7 0 x 4 = 280 8 0 x 4 = 320 8 0 5 7 8 9 0 x 2 = 180 9 2 6 10 0 0 10 0 x 2 = 200 15 5 0

  19. Finding the Mean (the average) 10 10 10 4 0 9 9 4 0 x 3 = 120 X X 10 5 6 8 9 5 0 x 3 = 150 X X X 10 6 0 x 5 = 300 6 1 X 4 X X 7 7 X 7 X 20 7 3 5 6 8 7 0 x 4 = 280 25 X X X 8 0 x 4 = 320 8 0 5 7 8 95 X X 9 0 x 2 = 180 9 X 2 6 10 0 0 10 0 x 2 = 200 15 5 0 + 117

  20. Finding the Mean (the average) We have 23 leaves. Divide your sum by 23. 4 0 9 9 5 6 8 9 1667 ÷ 23 = 6 1 4 7 7 7 7 3 5 6 8 Mean: Approximately 72.48 8 0 5 7 8 9 2 6 10 0 0 15 5 0 + 117

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