Learning Activities (2) | Classroom Resources (5) |

View Standards
**Standard(s): **
[MA2015] PRE (9-12) 41 :

41 ) Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve. [S-ID4]

Students will work through a Desmos activity on Normal Distribution. They will be reminded of how to find the mean of a data set. The process of finding the standard deviation of a set of data values will be introduced. Students will practice doing both calculations. Next, using the mean and standard deviation they will define the intervals in a normal curve and will approximate the percentage of items in each interval using the Empirical Rule.

*This activity results from the ALEX Resource Development Summit.*

41 ) Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve. [S-ID4]

Students will work through a Desmos activity on Normal Distribution. They will be reminded of how to find the mean and standard deviation of a data set. Students will practice doing both calculations. Next, using the mean and standard deviation they will define the intervals in a normal curve and will approximate the percentage of items in each interval using the Empirical Rule.

*This activity results from the ALEX Resource Development Summit.*

View Standards
**Standard(s): **
[MA2015] AL1 (9-12) 41 :

[MA2015] AL1 (9-12) 42 :

[MA2015] AL1 (9-12) 43 :

[MA2015] PRE (9-12) 45 :

[MA2015] PRE (9-12) 46 :

[MA2015] PRE (9-12) 49 :

[MA2015] PRE (9-12) 40 :

[MA2015] PRE (9-12) 39 :

[MA2015] PRE (9-12) 41 :

41 ) Represent data with plots on the real number line (dot plots, histograms, and box plots). [S-ID1]

[MA2015] AL1 (9-12) 42 :

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) 45 :

45 ) Decide if a specified model is consistent with results from a given data-generating process, e.g., using simulation. [S-IC2]

Example: A model says a spinning coin falls heads up with probability 0.5. Would a result of 5 tails in a row cause you to question the model'

[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) 49 :

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

[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)

[MA2015] PRE (9-12) 41 :

41 ) Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve. [S-ID4]

One way we analyze data is to look at measures of central tendency—mean, median, and mode. They are the tools to look at the information for the purpose of answering the question, “What is normal?” Understanding the measures of central tendency can help us make important life decisions. For example, averages can help us set goals or plan budgets. At the end of this lesson about central tendency, students will be able to recognize and apply the concepts of mean, median, and mode in real-life problems.

View Standards
**Standard(s): **
[MA2015] AL1 (9-12) 41 :

[MA2015] AL1 (9-12) 42 :

[MA2015] AL1 (9-12) 43 :

[MA2015] PRE (9-12) 46 :

[MA2015] PRE (9-12) 40 :

[MA2015] PRE (9-12) 39 :

[MA2015] PRE (9-12) 41 :41 ) Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve. [S-ID4]

41 ) Represent data with plots on the real number line (dot plots, histograms, and box plots). [S-ID1]

[MA2015] AL1 (9-12) 42 :

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) 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) 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)

[MA2015] PRE (9-12) 41 :

Introduce high school students to the art and science of statistics in the 6-minute video, "What is Statistics?" from the Against All Odds series. This video resource will demonstrate how gathering, organizing, drawing, and analyzing data is applicable in everyday life and a variety of careers.

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

[MA2015] AL1 (9-12) 43 :

[MA2015] AL2 (9-12) 37 :

[MA2015] ALT (9-12) 41 :

[MA2015] PRE (9-12) 40 :

[MA2015] PRE (9-12) 39 :

[MA2015] PRE (9-12) 41 :41 ) Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve. [S-ID4]

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] AL2 (9-12) 37 :

37 ) (+) Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator). [S-MD6]

[MA2015] ALT (9-12) 41 :

41 ) (+) Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator). [S-MD6]

[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)

[MA2015] PRE (9-12) 41 :

Discover how calculating median and mean reveal different ways to describe a center of distribution in this 9-minute video from the Against All Odds statistics series. This video resource will examine differences in comparable wages for men and women to see practical applications of statistics and data visualization.

View Standards
**Standard(s): **
[MA2015] AL1 (9-12) 42 : 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) 45 :

[MA2015] PRE (9-12) 46 :

[MA2015] PRE (9-12) 47 :

[MA2015] PRE (9-12) 48 :

[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)

[MA2015] PRE (9-12) 41 :41 ) Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve. [S-ID4]

[MA2015] AL1 (9-12) 43 :

[MA2015] PRE (9-12) 45 :

45 ) Decide if a specified model is consistent with results from a given data-generating process, e.g., using simulation. [S-IC2]

Example: A model says a spinning coin falls heads up with probability 0.5. Would a result of 5 tails in a row cause you to question the model'

[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) 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 :

[MA2015] PRE (9-12) 39 :

[MA2015] PRE (9-12) 41 :

This exercise was developed to complement the film *The National Parks of Texas* by Texas PBS & Villita Media. In this activity, students will learn about estimating the number of trees in a large area based on a smaller area.

This is one way statisticians measure forests and other wide expanses of land. It's also a great way to illustrate how polling works. Scientists will interview a smaller sample size of Americans, rather than every single American, and then make estimations based on their results. In the same way, we counted smaller samples of trees, rather than all of the trees individually to get an estimate of how many trees are in the park total.

**Note: The corresponding lesson plan can be found under the "Support Materials for Teachers" link on the right side of the page. **

This topic introduces students to the idea of using a smooth curve to model a data distribution, eventually leading to using the normal distribution to model data distributions that are bell-shaped and symmetric. Many naturally occurring variables, such as arm span, weight, reaction times, and standardized test scores, have distributions that are well described by a normal curve. Students begin by reviewing their previous work with shape, center, and variability. Students use the mean and standard deviation to describe center and variability for a data distribution that is approximately symmetric. This provides a foundation for selecting an appropriate normal distribution to model a given data distribution. Students learn to draw a smooth curve that could be used to model a given data distribution. A smooth curve is first used to model a relative frequency histogram, which shows that the area under the curve represents the approximate proportion of data falling in a given interval. Properties of the normal distribution are introduced by asking students to distinguish between reasonable and unreasonable data distributions for using a normal distribution model. Students use tables and technology to calculate normal probabilities. They work with graphing calculators, tables of normal curve areas, and spreadsheets to calculate probabilities in the examples and exercises provided (S-ID.A.4).

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