Stem and Leaf Stem Plots

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How to Draw Stem Plots, How to read them, ansd how to find the Median from them. Includes Groups of Five S&L Plots.

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http://passyworldofmathematics.com/pwerpoints/

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Stem and Leaf Stem Plots

  1. 1. Stem and Leaf PlotsKey : 5 | 6 = 56 hoursSTEM LEAF 0 4 5 5 7 1 0 4 5 5 7 2 0 2 3 6 7 3 2 4 6 4 5 6 6 7 5 Camera and Battery Images from Google Images
  2. 2. Camera Battery Life TestingA magazine did some testing to see how long camera batteries lasted before they needed recharging. (Several cameras and test conditions were used).The results, measured in number of hours until a camera’s battery was flat, were as follows: 26, 32, 14, 10, 5, 34, 4, 7, 15, 17, 15, 22, 27, 20, 23, 36, 5, 56, 75
  3. 3. Organising Battery Life Test ResultsOur first step in analysing this data is to construct a Frequency Table of the results.26, 32, 14, 10, 5, 34, 4, 7, 15, 17, 15, 22, 27, 20, 23, 36, 5, 56, 75The Highest value is 75, and the lowest value is 4.This gives a Range of 75 - 4 = 71.Size of Class Intervals = Range / 10 = 71 divided by 10 = 7.1 = 7Seven is not the easiest of numbers to work with, and so we have decided to group our data into Groups of 10.
  4. 4. Frequency Table for Battery LifeBattery Life FREQUENCY Actual Values Here is the Frequency 0-9 4 4, 5, 5, 7 Table for our camera 10-19 5 10, 14, 15, 15, 17 battery test results: 20-29 5 20, 22, 23, 26, 27 30-39 3 32, 34, 36 26, 32, 14, 10, 5, 34, 40-49 0 4, 7, 15, 17, 15, 22, 50-59 1 56 27, 20, 23, 36, 5, 60-69 0 56, 75 70-79 1 75
  5. 5. Bar Graph for Battery LifeBattery Life FREQUENCY0-9 410-19 520-29 530-39 340-49 050-59 160-69 070-79 1(The Horizontal Bar Chart for our results, made using “Chart Go”.)
  6. 6. Stem and Leaf Diagram to show camera battery life under various conditions Key : 5 | 6 = 56 hoursBattery Life Actual Values STEM LEAF0-9 4, 5, 5, 7 Ones 0 4 5 5 710-19 10, 14, 15, 15, 17 Tens 1 0 4 5 5 720-29 20, 22, 23, 26, 27 Twenties 2 0 2 3 6 730-39 32, 34, 36 Thirties 3 2 4 640-49 Fourties 450-59 56 Fifties 5 660-69 Sixties 670-79 75 Seventies 7 5
  7. 7. The Structure and Values for a Stem and Leaf DiagramIn a Stem and LeafPlot, the datavalues are put in Key : 5 | 6 = 56 hoursorder from theLowest to Highest. Battery Life Data Values STEM LEAFWe then group 0-9them into : 4, 5, 5, 7 Ones 0 4 5 5 7 10-19 10, 14, 15, 15, 17 Tens 1 0 4 5 5 7Ones = 0 to 9 20-29Tens = 10 to 19 20, 22, 23, 26, 27 Twenties 2 0 2 3 6 7and so on. These 3 2 4 6 30-39 32, 34, 36 Thirtiesgroups are calledthe40-49 “Stems”. Fourties 4 50-59 56 Fifties 5 6The “Leaf” is the 60-69last digit on each Sixties 6of the original 7 5 70-79 75 Seventiesdata values.
  8. 8. Bar Chart and Stem & Leaf Diagram for Camera Battery Life TestingNotice how the Bar Chart and the S&LDiagram have the same overall shape. Key : 5 | 6 = 56 hours STEM LEAF 0 4 5 5 7 1 0 4 5 5 7 2 0 2 3 6 7 3 2 4 6 4 5 6 6 7 5
  9. 9. Stem and Leaf Plot Values and ShapeKey : 5 | 6 = 56 hours STEM LEAF 0 4 5 5 7 1 0 4 5 5 7 2 0 2 3 6 7 3 2 4 6 A Stem and Leaf Plot puts all of the data values into order, and places 4 them in groups. It also has the same 5 6 shape as a Bar Chart of the data. 6 7 5 It is like a Bar Chart, but with the data values written onto it, instead of having coloured bars.
  10. 10. Reading Stem and Leaf PlotsSTEM LEAF 0 4 5 5 7 Ones 0|5 = 5 1 0 4 5 5 7 2 0 2 3 6 7 Twenties 2|6 = 26 (Not 6) 3 2 4 6 4 5 6 Fifties 5|6 = 56 (Not 6) 6 7 5 Key : 5 | 6 = 56 hours
  11. 11. Stem and Leaf – Maximum and Minimum The Minimum value is alwaysSTEM LEAF at the start of the S&L Plot: 0 4 5 5 7 0|4 = 4 1 0 4 5 5 7 The Maximum value is 2 0 2 3 6 7 always at the end of the S&L 3 2 4 6 plot: 7|5 = 75 4 5 6 The S&L contains 19 values, (not 27 values). 6 7 5 Eg. Only count how many Leaves there are. Key : 5 | 6 = 56 hours
  12. 12. Stem and Leaf – Median AverageSTEM LEAF Because the data values 0 4 5 5 7 are in order, (from lowest 1 0 4 5 5 7 to highest), we can easily 2 0 2 3 6 7 find the middle “Median” 3 2 4 6 by crossing off values from 4 each end, until we reach 5 6 the middle value. 6 7 5 Median = 20 hours Key : 5 | 6 = 56 hours
  13. 13. Stem and Leaf – Double Medians For our Camera Battery LifeSTEM LEAF results, we had 19 results contained in the leaves. 0 4 5 5 7 1 0 4 5 5 7 Whenever we have an ODD number of items like this, there 2 0 2 3 6 7 is always only one middle 3 2 4 6 number which is the “Median”. 4 The next example shows an 5 6 EVEN number of items. 6 For an EVEN number of 7 5 items, we will always have two middle numbers. Key : 5 | 6 = 56 hours
  14. 14. Stem and Leaf – Double Medians Here is a different set of BatterySTEM LEAF Life results, where we have 22 0 4 5 5 7 results contained in the leaves. 1 0 4 5 5 7 Whenever we have an EVEN 2 0 2 3 6 7 number of items like this, there 3 2 4 6 are always two middle numbers. 4 We find the midpoint of these 5 6 6 9 two numbers by adding them 6 together and dividing by 2. 7 5 8 Median = ( 22 + 23 ) / 2 Key : 5 | 6 = 56 hours Median = 22.5 hours.
  15. 15. Making a Stem and Leaf PlotOur original Battery Testing results were as follows:26, 32, 14, 10, 5, 34, 4, 7, 15, 17, 15, 22, 27, 20, 23, 36, 5, 56, 75We need to separate out these results into Groups of 10. Ones 5, 4, 7, 5 Tens 14, 10, 15, 17, 15 Twenties 26, 22, 27, 20, 23 Next we need to set up Thirties 32, 34, 36 stems for the ones Fifties 56 through to the seventies. Seventies 75 (See next slide)
  16. 16. Making a Stem and Leaf PlotOnes 5, 4, 7, 5 STEM LEAFTens 14, 10, 15, 17, 15 0 1Twenties 26, 22, 27, 20, 23 2Thirties 32, 34, 36 3Fourties 4 5Fifties 56 6Sixties 7Seventies 75Next we need to set up Leaves for all of the original values. (See next slide)
  17. 17. Making a Stem and Leaf PlotOnes 5, 4, 7, 5 STEM LEAFTens 14, 10, 15, 17, 15 0 5 4 7 5 1 4 0 5 7 5Twenties 26, 22, 27, 20, 23 2 6 2 7 0 3Thirties 32, 34, 36 3 2 4 6Fourties 4 5 6Fifties 56 6Sixties 7 5Seventies 75We only take the last digit of each data value when making the leaves.
  18. 18. Unordered Stem and Leaf PlotSTEM LEAF Our Stem and Leaf Plot 0 5 4 7 5 does not have our data 1 4 0 5 7 5 placed into order from 2 6 2 7 0 3 lowest to highest. 3 2 4 6 4 5 6 We call this plot an 6 “Unordered Stem and 7 5 Leaf Plot”.Key : 5 | 6 = 56 hours
  19. 19. Ordered Stem and Leaf Plot STEM LEAF STEM LEAF 0 5 4 7 5 0 4 5 5 7 1 4 0 5 7 5 1 0 4 5 5 7 2 6 2 7 0 3 Place 2 0 2 3 6 7 3 2 4 6 the 3 2 4 6 4 leaves 4 into 5 6 5 6 order 6 6 7 5 7 5 Key : 5 | 6 = 56 hours Key : 5 | 6 = 56 hoursUnordered Stem and Leaf Plot Ordered Stem and Leaf Plot
  20. 20. Groups of Five S&L Plot Groups of Five Stem and Leaf STEM LEAF Plot 0 4 0* 5 5 7Groups of Ten S&L Plot 1 0 4 1* 5 5 7 STEM LEAF 2 0 2 3 0 4 5 5 7 Split 2* 6 7 1 0 4 5 5 7 each 3 2 4 2 0 2 3 6 7 group 3* 6 3 2 4 6 of ten 4 4 in half 5 5 6 5* 6 6 6 7 5 7 7* 5
  21. 21. Groups of Five S&L Plot Groups of Five Stem and Leaf STEM LEAF Plot 0 4 0 to 4 * 5 to 9 0* 5 5 7In a Groups of Five S&L 10 to 14 1 0 4Plot, the groups each * 15 to 19 1* 5 5 7contain a range of five. 20 to 24 2 0 2 30 to 4 = 0,1,2,3,4 = five * 25 to 29 2* 6 7items (count them on 30 to 34 3 2 4your fingers). * 35 to 39 3* 6The tens, for example 40 to 44 4have a lower range of * 45 to 49 4*10 to 14 named as 1 | 50 to 54 5and * 55 to 59 5*an upper range of15 to 19 named as 1* | etc
  22. 22. Stem and Leaf Plot - SUMMARY• Stem and Leaf Plots have data placed into order from lowest to highest.• They consist of a Stem Column (in tens) and a Leaf Column that has last digits only• Because the data is in order, we can cross off forward and backward and find the Median• The shape of the S&L Plot is the same as a horizontal Bar Chart of the data.
  23. 23. http://passyworldofmathematics.com/

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