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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. ★
Standard #: MAFS.912.S-ID.1.4Archived Standard
Standard Information
General Information
Subject Area: Mathematics
Grade: 912
Domain-Subdomain: Statistics & Probability: Interpreting Categorical & Quantitative Data
Cluster: Level 2: Basic Application of Skills & Concepts
Cluster: Summarize, represent, and interpret data on a single count or measurement variable. (Algebra 1 - Additional Cluster) (Algebra 2 - Additional Cluster) -

Clusters should not be sorted from Major to Supporting and then taught in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.
Date Adopted or Revised: 02/14
Content Complexity Rating: Level 2: Basic Application of Skills & Concepts - More Information
Date of Last Rating: 02/14
Status: State Board Approved - Archived
Related Courses
Related Resources
Formative Assessments
  • Probability of Your Next Texting Thread # Students are asked to find the probability that an outcome of a normally distributed variable is greater than a given value.
  • Range of Texting Thread # Students are asked to find the probability that an outcome of a normally distributed variable is between a standard deviation level.
  • Label a Normal Curve # Students are asked to scale and label a normal curve given the mean and standard deviation of a data set with a normal distribution.
  • Area Under the Normal Curve # Students are asked to find the probability that an outcome of a normally distributed variable is between two given values using both a Standard Normal Distribution Table and technology.
  • Algebra Test Scores # Students are asked to select a histogram for which it would be appropriate to apply the 68-95-99.7 rule.
Lesson Plans
  • Sensoring Data # In this follow up lesson, students will explore data collection using the weather station sensor and perform statistical analysis of the data. Students will use a scientific method of inquiry to plan an investigation of their own. This activity is meant to allow students to use a variety of skills they have acquired throughout a statistics unit in a personally meaningful way.
  • Show Me the Money! Selecting Student Athletes for Scholarships # In this Model Eliciting Activity, MEA, students will use data to decide the ideal candidate for a college scholarship by computing the mean and the standard deviation. The student will present the data using the normal distribution and make recommendations based on the findings. Students will recognize that not all data can be presented in this format. Model-Eliciting-Activities, MEAs, allow students to critically analyze data sets, compare information, and require students to explain their thinking and reasoning. While there is no one correct answer in an MEA, students should work to explain their thinking clearly and rationally. Therefore, teachers should ask probing questions and provide feedback to help students develop a coherent, data-as-evidence-based approach within this learning experience.
  • College Freshman Entrance Data # An introduction to classifying data as normally distributed, skewed left, or skewed right, Technology is used to calculate the mean, median, and standard deviation. Data listing ranking, acceptance rates, average GPA, SAT and ACT scores, and tuition rates from 36 Universities are used.
  • Standard Deviation and the Normal Curve in Kahoot! # In this three-day lesson, students learn about standard deviation, the normal curve, and how they are applied. Your students will be engaged and learning when they collect and analyze data using a free Kahoot! quiz.
  • Picturing the Normal World # This is an introductory lesson on normally distributed data. Students will calculate the standard deviation and use the Empirical Rule.
  • How do we measure success? # Students will use the normal distribution to estimate population percentages and calculate the values that fall within one, two, and three standard deviations of the mean. Students use statistics and a normal distribution to determine how well a participant performed in a math competition.
  • If The Shoe Fits – A "Normal" Cinderella Story # Using a normal distribution manipulative and a calculator, students will explore the normal distribution curve to determine the area between each standard deviation from the mean using the empirical rule. Students will use the mean and standard deviation to predict outcomes in real-world situations and finally answer the age old question: What size was Cinderella's glass slipper?
  • Sensoring Data # In this follow up lesson, students will explore data collection using the weather station sensor and perform statistical analysis of the data. Students will use a scientific method of inquiry to plan an investigation of their own. This activity is meant to allow students to use a variety of skills they have acquired throughout a statistics unit in a personally meaningful way.
  • Representing Data 1: Using Frequency Graphs # This lesson unit is intended to help you assess how well students are able to use frequency graphs to identify a range of measures, make sense of this data in a real-world context, and understand that a large number of data points allow a frequency graph to be approximated by a continuous distribution.
  • Representing Data 2: Using Box Plots # This lesson unit is intended to help you assess how well students are able to interpret data using frequency graphs and box plots. In particular, this unit aims to identify and help students who have difficulty figuring out the data points and spread of data from frequency graphs and box plots. It is advisable to use the first lesson in the unit, Representing Data 1: Frequency Graphs (32498), before this one.
Perspectives Video: Professional/Enthusiasts
Perspectives Video: Teaching Idea
  • Smile Statistics # <p>This quantitative measurement and statistics activity will allow you to save face.</p>
Problem-Solving Tasks
  • SAT Scores # This problem solving task challenges students to answer probability questions about SAT scores, using distribution and mean to solve the problem.
  • Should We Send Out a Certificate? # The purpose of this task is to have students complete normal distribution calculations and to use properties of normal distributions to draw conclusions.
  • Do You Fit in This Car? # This task requires students to use the normal distribution as a model for a data distribution. Students must use given means and standard deviations to approximate population percentages.
Virtual Manipulative
  • Normal Distribution Interactive Activity # With this online tool, students adjust the standard deviation and sample size of a normal distribution to see how it will affect a histogram of that distribution. This activity allows students to explore the effect of changing the sample size in an experiment and the effect of changing the standard deviation of a normal distribution. Tabs at the top of the page provide access to supplemental materials, including background information about the topics covered, a description of how to use the application, and exploration questions for use with the java applet.
STEM Lessons - Model Eliciting Activity
  • Show Me the Money! Selecting Student Athletes for Scholarships # In this Model Eliciting Activity, MEA, students will use data to decide the ideal candidate for a college scholarship by computing the mean and the standard deviation. The student will present the data using the normal distribution and make recommendations based on the findings. Students will recognize that not all data can be presented in this format. Model-Eliciting-Activities, MEAs, allow students to critically analyze data sets, compare information, and require students to explain their thinking and reasoning. While there is no one correct answer in an MEA, students should work to explain their thinking clearly and rationally. Therefore, teachers should ask probing questions and provide feedback to help students develop a coherent, data-as-evidence-based approach within this learning experience.
MFAS Formative Assessments
  • Algebra Test Scores # Students are asked to select a histogram for which it would be appropriate to apply the 68-95-99.7 rule.
  • Area Under the Normal Curve # Students are asked to find the probability that an outcome of a normally distributed variable is between two given values using both a Standard Normal Distribution Table and technology.
  • Label a Normal Curve # Students are asked to scale and label a normal curve given the mean and standard deviation of a data set with a normal distribution.
  • Probability of Your Next Texting Thread # Students are asked to find the probability that an outcome of a normally distributed variable is greater than a given value.
  • Range of Texting Thread # Students are asked to find the probability that an outcome of a normally distributed variable is between a standard deviation level.
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