Classroom Resources (8) |

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 ) 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 :

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]

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 :

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 :

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]

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. **

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) 44 :

[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 :

[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] AL1 (9-12) 43 :

[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 :

[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 :

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] 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 :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 :

[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] 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 :

[MA2015] PRE (9-12) 49 :

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

[MA2015] PRE (9-12) 40 :

[MA2015] PRE (9-12) 39 :

Real-world examples demonstrate the benefits of histograms in this 10-minute video from the Against All Odds statistics series. Data visualization techniques help students understand the practical application of statistics in meteorology and in predicting traffic patterns. Hosted by Pardis Sabeti, this series walks students through understanding how statistics are used in everyday life.

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

[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]

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

[MA2015] AL1 (9-12) 42 :

[MA2015] AL1 (9-12) 43 :

In Module 2, Topic A, students observe and describe data distributions. They reconnect with their earlier study of distributions in Grade 6 by calculating measures of center and describing overall patterns or shapes. Students deepen their understanding of data distributions recognizing that the value of the mean and median are different for skewed distributions and similar for symmetrical distributions. Students select a measure of center based on the distribution shape to appropriately describe a typical value for the data distribution. Topic A moves from the general descriptions used in Grade 6 to more specific descriptions of the shape and the center of data distribution.

[MA2015] AL1 (9-12) 42 :

[MA2015] AL1 (9-12) 43 :

In Module 2, Topic B, students reconnect with methods for describing variability first seen in Grade 6. Topic B deepens students’ understanding of measures of variability by connecting a measure of the center of the data distribution to an appropriate measure of variability. The mean is used as a measure of center when the distribution is more symmetrical. Students calculate and interpret the mean absolute deviation and the standard deviation to describe variability for data distributions that are approximately symmetric. The median is used as a measure of center for distributions that are more skewed, and students interpret the interquartile range as a measure of variability for data distributions that are not symmetric. Students match histograms to box plots for various distributions based on an understanding of center and variability. Students describe data distributions in terms of shape, a measure of center, and a measure of variability from the center.