Transcript chapter 16. data analysis, statistics, and probability

The Data Analysis and
Probability Standard
Principles and Standards for School
Mathematics
National Council of Teachers of
Mathematics
2000
Instructional programs from pre-kindergarten
through grade 12 should enable all students to
Formulate questions that can be addressed with
data and collect, organize, and display relevant
data to answer them.
Select and use appropriate statistical methods to
analyze data.
Develop and evaluate inferences and predictions
that are based on data.
Understand and apply basic concepts of
probability.
Why Teach Statistics and
Probability?
1. Children encounter ideas of statistics and
probability outside of school every day.
2. Statistics and probability provide
connections to other mathematics topics or
school subjects.
3. Statistics and probability provide
opportunities for computational activity in
a meaningful setting.
Four Steps of Data Analysis
Pose a question and collect data.
Display data.
Analyze data.
Communicate results.
Descriptive Statistics
Measure of Variation
Range - the variation or spread or a set of data
Measures of Central Tendency or Averages
Mode-the value that occurs most frequently
Median-the middle value in a set of data
Mean-the arithmetic average
Probability
Probability of an Event
Events or Outcomes
Certain/Uncertain
Impossible
Likely/Unlikely
Sample Space
Randomness
Fair/Unfair
Independence of Events
Mystery Bags
Open your mystery bag but do not look inside.
Shake the contents, reach in and pull out one
color tile. Record the color of the tile chosen
and return it to the bag.
Repeat this process 9 more times, recording
each result.
Based on these 10 trials, how many of each
color of tile are in your bag? (Remember there
are a total of 12 tiles in the bag.)
Mystery Bags
Conduct 10 more trials using the same
process of random selection from the
bag.
Now, based on 20 trials, how many of
each color does your bag contain? Is this
different from your previous guess?
Mystery Bags
Based on your experiment, what is the
probability that the tile chosen will be
red? yellow? blue? green?
Open the bag and look at the contents.
How well did your experimentation
reveal the actual contents of the bag?