Transcript Probability - Thefutureteacher

Mathematics
Domain 2 Competency 17
Probability and Statistics
What’s the goal of this
competency?
• The teacher understands concepts related
to probability and statistics and their
applications.
Key Definitions
Statistics – The branch of mathematics
that deals with the collection,
organization, analysis, and interpretation
of numerical data. It is the science or the
study of data.
Probability- The ratio of the number of
outcomes in an exhaustive set of equally
likely outcomes that produce a given
event to the total number of possible
outcomes. It gives us a way to measure
uncertainty.
How do probability and statistics
relate to each other?
DATA ANALYSIS
– Involves both probability and statistics.
Examples of probability in the real
world.
- Weather Forecasting
- Batting Averages
- Winning the Lottery
- Insurance premium calculation
Data Set Descriptors 1
•
Range -The range of a set of data is the difference
between the highest and lowest values in the set. To
find the range, first order the data from least to
greatest. Then subtract the smallest value from the
largest value in the set.
Example
Problem: Cheryl took 7 math tests in one marking
period. What is the range of her test
scores?
89, 73, 84, 91, 87, 77, 94
Solution: Ordering the test scores from least to
greatest, we get: 73, 77, 84, 87, 89, 91, 94 highest
- lowest = 94 - 73 = 21
Answer: The range of these test scores is 21 points.
Data Set Descriptors 2
• Mean – The mean of a set of data is found by
taking the sum of the data and dividing by the
total number of values in the set. The mean is
commonly referred to as the average.
Example
Problem: Scott took 7 math tests in one
marking period. What is the mean test
score?
89, 73, 84, 91, 87, 77, 94
Solution: The sum of these numbers is 595.
Dividing the sum by the number of test scores
we get:
595 divided by 7
Answer: The mean test score is 85.
Data Set Descriptors 3
• Median-The median of a set of data is the
middlemost number in the set. The median is also
the number that is halfway into the set. To find
the median, the data should first be arranged in
order from least to greatest.
Example
Problem: The Doran family has 5 children, aged
9, 12, 7, 16 and 13. What is the age of the middle
child?
Solution: Ordering the childrens' ages from least
to greatest, we get: 7, 9, 12, 13, 16
Answer: The age of the middle child is the
middlemost number in the data set, which is 12.
Data Set Descriptors 4
• Mode- The mode of a set of data is the value in
the set that occurs most often.
Example
Problem: The number of points scored in a
series of football games is listed below. Which
score occurred most often?
7, 13, 18, 24, 9, 3, 18
Solution: Ordering the scores from least to
greatest, we get: 3, 7, 9, 13, 18, 18, 24
Answer: The score which occurs most often is 18.
Basics for Elementary School
Students
•
Concert examples are better for this age group,
the students need real problems and/or
simulations.
Steps for an Experiment
1. Data Collections
2. Sampling
3. 3.Organizing and Representing Data
4. Interpreting Data
5. Assigning Probabilities
6. Making Inferences
Probability Formula
• Probability is a way of describing how likely it is
a particular outcome will occur.
• Probability results (fraction)=
Number of favorable outcomes
(numerator)
Total number of possible outcomes (denominator)
Coin Toss Example
Probability –Gauge of Understanding
1) Use of experimental and theoretical probability
to make predictions.
2) Use of statistical representations to analyze data.
Sample Set
The set of all possible outcomes of an
experiment.
Permutations
All possible arrangements of a given number of
items in which the order of the items make a
difference.
Ex: Different ways a set of four books can be
placed on a shelf.
Jones, Langral, Thornton and Mogill
4 Stages of the Learning Process –Probability
Subjective Level- Learners easily swayed by personal
experiences when making probabilistic
statements.
Second Level- Transitional learners begin to
organize the importance of organizing
information.
Third Level- Students begin to become informal
quantitative thinkers.
Numerical Level- Students understand the nuances
of numerical argument and use sophisticated
procedures to determine numerical facts.
Sample Lesson
Data Displays
Students will utilize and interpret:
• Tables
• Bar Graphs
• Circle Graphs
• Line plot
• Pictographs
to compare data through finding the
means, medians, and modes of the
information presented.