06 Likely-ness (and some fractions) Science By the Horns

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06 Likely-ness(and some fractions) Science By
the Horns

• Summer 2006

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Overview

• Histograms and Representing Likeliness

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Histograms
Start with Categorical Start with post-it notes
Favorite Color? Which is most favorite? Most
likely? (if want to bet on what a new person in
class will say, what would you bet?)
Likely-ness
Trials
green
yellow
red
blue
brown
Possibilities
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What Questions Can we Ask?
__ out of ___ trials are ___ __ out of ___
trials are ___ __ out of ___ trials are ___ or
__ Bigger means what? (hint at more likely)
Hint at fraction notation 2 out of 9 trials are
blue 2/9 are blue.
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Activity
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Sample from Bag/Box

• Hold bag for next person
• who then pulls out one block and writes color on
  post it note
• Now this person shakes and holds for next person
• Each student places post-it note

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Empirical Likely-Ness

• Build a histogram of results
• Explore
• What do you notice?
• Why do we see this? (how come not all the same?)
• __ out of __ are __
• Which most likely
• What if we did it again, what might we see

red
black
blue
orange
green
yellow
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Theoretical Likely-Ness

• If we know how much of each kind we have, we can
  represent the likely-ness this way.
• Explore
• What do you notice?
• Why do we see this? (how come not all the same?)
• __ out of __ are __
• Which most likely?

red
black
blue
orange
green
yellow
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Compare
empirical
theoretical
How similar? Different? Would it be exactly the
same if we did it again?
red
red
black
black
blue
blue
orange
orange
green
green
yellow
yellow
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Likeliness Discussion

• Each Group Makes its Own
• With Green the Most Likely

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Theoretical
Group Number Red Number Orange Number Black Number Yellow Number Green Number Blue Total
1 2 4 5 2 7 2
2 6 3 4 2 8 5
3 1 1 5 3 8 4
4 2 3 6 3 7 1
5 2 4 3 4 8 1
6 1 4 6 1 8 2
Totals 2 3 3 4 8 2
Fraction of all 3 3 3 3 8 2
Decimal of all 3 3 4 5 6 1
Denominator Of Fraction All
When done, copy blue cells
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Theoretical
(Double click graph above, paste in blue
values under Graph menu Quit)
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Sample from Combined

• Each group takes from box more than once
• Keep track of how many of each color for your
  group

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Empirical
Group Number Red Number Orange Number Black Number Yellow Number Green Number Blue Total
1
2
3
4
5
6
Totals
Fraction of all
Decimal of all
Denominator Of Fraction All
When done, copy blue cells
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Empirical
(Double click graph above, paste in blue
values under Graph menu Quit)