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Unit 2, Section 4: What’s Normal?

Instructional Days: 5

Enduring Understandings

Students learn that the Normal curve can be used as a model that describes many real phenomena. Drawing plots of the Normal curve over histograms helps data scientists determine if the distribution represented by the histogram is close to Normal. The Normal curve suggests that one is more likely to obtain values that are close to typical (average), which are found in the center of the curve, and less likely to obtain values that are extreme and farther away from typical.

Engagement

Students will learn about the Normal curve by watching the first 35 seconds the New York Times Video “Bunnies, Dragons, and the Normal World” found at: http://www.nytimes.com/video/science/100000002452709/bunnies-dragons-and-the-normal-world.html

Learning Objectives

Statistical/Mathematical:

S-ID 4: Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Understand that there are data sets for which such a procedure is not appropriate. Use calculators and RStudio to estimate areas under the normal curve.

S-IC 6: Evaluate reports based on data.

Data Science:

Learn to eyeball Normal distributions and overlay a Normal curve on a histogram; learn to simulate draws from a Normal distribution, and the impact of sample size; learn that estimating probabilities with a model leads to stable estimates; and estimate probabilities by finding the area under the Normal curve using RStudio.

Applied Computational Thinking Using RStudio:

• Use software to find the area under a Normal curve

• Use software to compare sample distributions (with histograms, for example) with the Normal distribution and make a decision as to whether the distribution appears Normally distributed.

• Draw random samples from a Normal distribution using software.

Real-World Connections:

The Normal curve is used to make inferences about a population. The model makes it possible to estimate the probability of occurrence of any value of a Normally distributed variable. For example, heights are Normally distributed. Using a Normal curve, we can find the probability of that a person would be a height of 6’ 2”.

Language Objectives

  1. Students will use complex sentences to construct summary statements about their understanding of data, how it is collected, how it used and how to work with it.

  2. Students will engage in partner and whole group discussions and presentations to express their understanding of data science concepts.

  3. Students will use complex sentences to write informative short reports that use data science concepts and skills.

Data File or Data Collection Method

Data Files:

  1. CDC data (cdc)

  2. Titanic data (titanic)

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