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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?