Oakridge International School
IB Diploma Programme
Class XII
Unit : Statistics and probability
Duration : 40 hrs
Syllabus requirements:
Statistics:
6.1. Concept of population, sample, random sample, and frequency distribution of discrete and
continuous data.
6.2. Presentation of data
6.3 Measures of spread
6.4 Cumulative frequency.
Elementry treatement for population, sample, random sample,and frequency distribution.Treatment of
both continuous and discrete data. Awareness that the population mean, μ, is generally unknown, and
that the sample mean, x, serves as an unbiased estimate of this quantity. Awareness of the concept of
dispersion and an understanding of the significance of the numerical value of the standard deviation.
Obtain the standard deviation (and indirectly the variance) from a GDC and by other methods.
Awareness that the population variance σ2 , is unknown, and that sn-12 = n sn2 serves as an unbiased
n 1
estimate of σ .
2
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Probability:
Chapter 15:
1. Introduction to Probability
2. Randomness
3. Sample space
4. Probability rules
5. Complement
6. Independence
7. Disjoint
8. Venndiagrams
9. Probability models
10.
Conditional probability
11.
Baye’s theorem
Chapter 17:
1. The Normal Distribution
2. Properties of normal curve
Chapter 16:
1. Discrete Random Variable
2. Mean and Variance
3. The Binomial Distribution
4. Hypergeometric Distribution
5. Poisson Distribution
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Approach:
Group presentations to be used for recap and reinforcement of the background knowledge.
Use of ICT: Students are to use PPTs to present their topics.
 Usefulness of GDC in finding the different measures of central tendency and also measures of spread is
taught to the students.
 Usage of MS Excel as a tool for graphing and regression is taught.
 PPTs used for presentation of different topics.
Considerations :
Statistics :
Exclusions for SL :- Discussion of bias of sn2 as an estimate of σ2
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Probability:
Relate the concepts of probability as the study of randomness.
Apply probability models to complex random phenomena.
Interpreting probability, including frequency interpretation.
Law of Large Numbers concept
Addition rule, multiplication rule, conditional probability and independence.
Discrete random variables and their probability distributions, binomial Hypergeometric and Poisson.
Understanding and calculate complex probabilities.
Continuous random variables and their probability distributions; Normal Distribution.
Standardization of normal distribution and InverseNorm.
Finding Quantiles
Exclusions for SL :- Hpergeometric and Poisson Distribution
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Guiding question(s) :
Statistics:
1.
2.
3.
4.
5.
6.
7.
8.
How does media conduct exit poll survey?
What are the measures that they use to come to conclusions?
What should a numeric summary include to describe any distribution?
What are the different formats to display distributions and when would each one be used?
Description of shape, center, spread.
What are the different ways to describe center?
What is an outlier?
How are mean and standard deviation affected by extrema?
Probability:
1. When/how is the addition rule applied?
2. What is the law of large numbers?
3. Can disjoint events be independent?
4. Define a binomial coefficient. Write out the general factorial expression. How are binomial coefficients
related to the tossing of a coin experiment?
5. What are appropriate conditions for using a Hypergeometric, binomial, or Poisson model?
6. What conditions must be satisfied to meet the definition of a Binomial, Hypergeometric and Poisson
distributions?
7. What is the significance of expected value in games of chance?
8. How do we compare two normal distributions?
9. Do probability distribution functions have inverse function?
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Learner Profile : Inquirers , Knowledgeable and Reflective
Information Literacy :
The students
 read and understand about the exit polls and research on the actual data collection/analysis that takes
place for exit polls.
 Understand the origin and history of probability through an assignment and classroom discussion.
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Discuss and understand the Type II Portfolio tasks : MODELLING THE HEIGHTS OF SAPLINGS and
MODELLING PROBABILITIES IN GAMES OF TENNIS .
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Learn how to use the IB information booklet for familiarizing themselves with the formulae in them and also use the Z and
InverseZ distribution tables.
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Learn using GDC for calculating PDF and CDF for binomial, hypergeometric, poisson and normal distributions.
International Mindedness:
The project on Peace and conflict of IB Community Theme, Sharing our humanity is to be done by the
students, where they research on different facts on major wars that took place in the last 50 years and
different statistical data is collected, analyzed and presented.
Differentiation:
Extra classes for slow learners.
HL and SL classes conducted separately.
Different level worksheets are given for Hl/SL.
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Resources:
IBID Text Book
Haese and Harris publications text book.
Power Point Presentations for
8 topics.
1. Introduction to probability
2. Compound events; Venn Diagrams
3. Probability rules
4. Independent events
5. Conditional Probability
6. Diagrammatic representation of probability
situations; Baye’s theorem
7. Random Variables; Discrete distributions
8. Continuous distributions
Web:
www.ibmaths.com
www.registatrt.co.uk/ib.html
http://www.statistics-helponline.com/node1.html
Assessment
 knowledge and understanding: Slip tests and oral
questioning.
 IA Skills
o : Regression analysis that is an important
tool in completing any portfolio is
taught/tested in this unit.
o Usage of GDC in statistical analysis and
calculation of probability distribution values
is tested in the unit testsand in the class room
 Formative : Oral questioning, Group presentation,
worksheets
 Summative : Unit test
Reflection/Review :
1. The group discussion worked out really well as
all the students got to participate and work on
their background knowledge.
2. The students were also taught regression analysis
as part of this course as that is required for them
to work on portfolio tasks.
3. Students who use TI-83 found it difficult to use it
for calculation PDF and CDF as compared to
Casio-fx8980.
AV:
Haese and Harris publications CD.
 Simulations of throwing of dice and throwing
of a coin.
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