Stem and leaf diagrams

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Stem and leaf diagrams

• Sometimes called stem and leaves too

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They really are as simple as they seem
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Simply a way of showing the values of data
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Example..

• Here are the weights of some aardvarks (kg)
• 12, 28, 17, 17, 19, 23, 9, 7, 25, 34, 21

• Stem and leaf might look like this
• Weight of aardvarks
• 0 9, 7
• 2, 7, 7, 9,
• 8, 3, 5, 1 KEY
• 4 1 2 is 12kg

STEM
LEAF OR LEAVES
Dont need to write this usually
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Your stem and leaf must have a

• Title
• Key so that other people can work out what your
  values are.

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An ordered stem and leaf.

• Has the values in size order.

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So for our example before

• Weight of aardvarks
• 0 9, 7
• 2, 7, 7, 9,
• 8, 3, 5, 1 KEY
• 4 1 2 is 12kg

• The ordered stem and leaf would be
• Weight of aardvarks
• 0 7, 9
• 2, 7, 7, 9,
• 1, 3, 5, 8 KEY
• 4 1 2 is 12kg

What weight does the 5 represent?
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Show the following data as a stem and leaf diagram

• I.Q. scores of Year 10 girls
• 105, 98, 112, 94, 130, 121, 98, 104, 100, 108,
  112, 104, 101, 97, 104

• I.Q. scores of Year 10 girls
• 9 8, 4, 8, 7
• 10 5, 4, 0, 8, 4, 1, 4
• 11 2, 2
• 12 1
• 13 0
• KEY
• 11 2 means 112

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Now order it

• I.Q. scores of Year 10 girls
• (unordered)
• 9 8, 4, 8, 7
• 10 5, 4, 0, 8, 4, 1, 4
• 11 2, 2
• 12 1
• 13 0
• KEY
• 11 2 means 112

• I.Q. scores of Year 10 girls
• (ordered)
• 9 4, 7, 8, 8
• 10 0, 1, 4, 4, 4, 5, 8
• 11 2, 2
• 12 1
• 13 0
• KEY
• 11 2 means 112

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The ordered one can be used to find lots of
information
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Mode.

• I.Q. scores of Year 10 girls
• (ordered)
• 9 4, 7, 8, 8
• 10 0, 1, 4, 4, 4, 5, 8
• 11 2, 2
• 12 1
• 13 0
• KEY
• 11 2 means 112

• Mode most common
• In this case 104

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Range .

• I.Q. scores of Year 10 girls
• (ordered)
• 9 4, 7, 8, 8
• 10 0, 1, 4, 4, 4, 5, 8
• 11 2, 2
• 12 1
• 13 0
• KEY
• 11 2 means 112

• Highest value lowest value
• In this case
• Range 130 94
• 36

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Median .

• I.Q. scores of Year 10 girls
• (ordered)
• 9 4, 7, 8, 8
• 10 0, 1, 4, 4, 4, 5, 8
• 11 2, 2
• 12 1
• 13 0
• KEY
• 11 2 means 112

• Put in size order (already done)
• then find the middle value
• In this case we have 15 values so we want the
• median 104

8th value along
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Lower Quartile .

• I.Q. scores of Year 10 girls
• (ordered)
• 9 4, 7, 8, 8
• 10 0, 1, 4, 4, 4, 5, 8
• 11 2, 2
• 12 1
• 13 0
• KEY
• 11 2 means 112

• Put in size order (already done)
• then find the value a quarter of the way up
• In this case we have 15 values so we want the
• Lower quartile 98

4th value along
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Upper Quartile .

• I.Q. scores of Year 10 girls
• (ordered)
• 9 4, 7, 8, 8
• 10 0, 1, 4, 4, 4, 5, 8
• 11 2, 2
• 12 1
• 13 0
• KEY
• 11 2 means 112

• Put in size order (already done)
• then find the value three- quarters of the way up
• In this case we have 15 values so we want the
• Upper quartile 112

12th value along
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You now know enough to be able to draw a box and
whisker diagram

• Smallest value Largest
  value
• median
• Lower quartile upper quartile

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Now for the boys..
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Show the following data as a stem and leaf diagram

• I.Q. scores of Year 10 boys
• 103, 98, 112, 99, 108, 122, 98, 104, 100, 108,
  112, 104, 101, 97, 104, 108, 99, 108, 102

• I.Q. scores of Year 10 boys
• 9 8, 9, 8, 7, 9
• 10 3,8,4,0,8,4,1,4,8,8,2
• 11 2, 2
• 12 2
• KEY
• 11 2 means 112

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Now order it

• I.Q. scores of Year 10 boys
• (unordered)
• 9 8, 9, 8, 7, 9
• 10 3,8,4,0,8,4,1,4,8,8,2
• 11 2, 2
• 12 2
• KEY
• 11 2 means 112

• I.Q. scores of Year 10 boys
• (ordered)
• 9 7, 8, 8, 9, 9
• 10 0,1,2,3,4,4,4,8,8,8,8
• 11 2, 2
• 12 2
• KEY
• 11 2 means 112

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Mode

• I.Q. scores of Year 10 boys
• 9 7, 8, 8, 9, 9
• 10 0,1,2,3,4,4,4,8,8,8,8
• 11 2, 2
• 12 2
• KEY
• 11 2 means 112

• Mode most common
• In this case 108

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Range

• I.Q. scores of Year 10 boys
• 9 7, 8, 8, 9, 9
• 10 0,1,2,3,4,4,4,8,8,8,8
• 11 2, 2
• 12 2
• KEY
• 11 2 means 112

• Highest value lowest value
• In this case
• Range 122 97
• 25

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Median

• I.Q. scores of Year 10 boys
• 9 7, 8, 8, 9, 9
• 10 0,1,2,3,4,4,4,8,8,8,8
• 11 2, 2
• 12 2
• KEY
• 11 2 means 112

• Put in size order (already done)
• then find the middle value
• In this case we have 19 values so we want the
• median 104

10th value
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Lower Quartile

• I.Q. scores of Year 10 boys
• 9 7, 8, 8, 9, 9
• 10 0,1,2,3,4,4,4,8,8,8,8
• 11 2, 2
• 12 2
• KEY
• 11 2 means 112

• Put in size order (already done)
• then find the value a quarter of the way up
• In this case we have 19 values so we want the
• Lower quartile 99

5th value
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Upper Quartile

• Put in size order (already done)
• then find the value three- quarters of the way up
• In this case we have 19 values so we want the
• Upper quartile 108

• I.Q. scores of Year 10 boys
• 9 7, 8, 8, 9, 9
• 10 0,1,2,3,4,4,4,8,8,8,8
• 11 2, 2
• 12 2
• KEY
• 11 2 means 112

15th value
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Now draw a box and whisker diagram to compare the
I.Q. of boys and girls

• you can draw this one on the same diagram as
  before.

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Here we go ..
What can you say about boys and girls I.Q.s ?
BOYS
GIRLS