Classroom Resources (2) |

View Standards
**Standard(s): **
[MA2015] AL1 (9-12) 42 :

[MA2015] AL1 (9-12) 43 :

[MA2015] PRE (9-12) 44 :

[MA2015] PRE (9-12) 46 :

[MA2015] PRE (9-12) 48 :

[MA2015] PRE (9-12) 40 :

[MA2015] PRE (9-12) 39 :

42 ) Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. [S-ID2]

[MA2015] AL1 (9-12) 43 :

43 ) Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers). [S-ID3]

[MA2015] PRE (9-12) 44 :

44 ) Understand statistics as a process for making inferences about population parameters based on a random sample from that population. [S-IC1]

[MA2015] PRE (9-12) 46 :

46 ) Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each. [S-IC3]

[MA2015] PRE (9-12) 48 :

48 ) Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant. [S-IC5]

[MA2015] PRE (9-12) 40 :

40 ) Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers). (*Identify unifrom, skewed, and normal distridutions in a set of data. Determine the quartiles and interquartile range for a set of data.*) [S-ID3] (Alabama)

[MA2015] PRE (9-12) 39 :

39 ) Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. (*Focus on increasing rigor using standard deviation*). [S-ID2] (Alabama)

Examine a mathematical theory known as the “wisdom of crowds,” which holds that a crowd’s predictive ability is greater than that of an individual, in this video from NOVA: *Prediction by the Numbers*. Sir Francis Galton documented this phenomenon after witnessing a weight-guessing contest more than a hundred years ago at a fair. Statistician Talithia Williams tests Galton’s theory with modern-day fairgoers, asking them to guess the number of jelly beans in a jar. Use this resource to stimulate thinking and questions about the use of statistics in everyday life and to make evidence-based claims about predictive ability.

View Standards
**Standard(s): **
[MA2015] PRE (9-12) 44 :

[MA2015] PRE (9-12) 46 :

[MA2015] PRE (9-12) 47 :

[MA2015] PRE (9-12) 49 :

44 ) Understand statistics as a process for making inferences about population parameters based on a random sample from that population. [S-IC1]

[MA2015] PRE (9-12) 46 :

46 ) Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each. [S-IC3]

[MA2015] PRE (9-12) 47 :

47 ) Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling. [S-IC4]

[MA2015] PRE (9-12) 49 :

49 ) Evaluate reports based on data. [S-IC6]

This topic introduces different types of statistical studies (e.g., observational studies, surveys, and experiments) (S-IC.B.3). The role of randomization (i.e., random selection in observational studies and surveys and random assignment in experiments) is addressed. A discussion of random selection (i.e., selecting a sample at random from a population of interest) shows students how selecting participants at random provides a representative sample, thereby allowing conclusions to be generalized from the sample to the population. A discussion of random assignment in experiments, which involves assigning subjects to experimental groups at random, helps students see that random assignment is designed to create comparable groups making it possible to assess the effects of an explanatory variable on a response.

The distinction between population characteristics and sample statistics (first made in Grade 7) is revisited. Scenarios are introduced in which students are asked a statistical question that involves estimating a population mean or a population proportion. For example, students are asked to define an appropriate population, population characteristic, sample, and sample statistics that might be used in a study of the time it takes students to run a quarter mile or a study of the proportion of national parks that contain bald eagle nests.

In this topic, students use data from a random sample to estimate a population mean or a population proportion. Building on what they learned about sampling variability in Grade 7, students use simulation to create an understanding of the margin of error. In Grade 7, students learned that the proportion of successes in a random sample from a population varies from sample to sample due to the random selection process. They understand that the value of the sample proportion is not exactly equal to the value of the population proportion. In Algebra II, they use margin of error to describe how different the value of the sample proportion might be from the value of the population proportion. Students begin by using a physical simulation process to carry out a simulation. Starting with a population that contains successes (using a bag with black beans and white beans), they select random samples from the population and calculate the sample proportion. By doing this many times, they are able to get a sense of what kind of differences are likely. Their understanding should then extend to include the concept of margin of error. Students then proceed to use technology to carry out a simulation. Once students understand the concept of margin of error, they go on to learn how to calculate and interpret it in context (S-IC.A.1, S-IC.B.4). Students also evaluate reports from the media in which sample data are used to estimate a population mean or proportion (S-IC.B.6).

**Note: Although this module is identified as Algebra II in the EngageNY curriculum, it corresponds to the Precalculus Alabama Course of Study.**