MA.912.DP.2.2

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.

Clarifications

Clarification 1: Instruction includes the connection to the binomial distribution and surveys.
General Information
Subject Area: Mathematics (B.E.S.T.)
Grade: 912
Strand: Data Analysis and Probability
Status: State Board Approved

Related Courses

This benchmark is part of these courses.
1210300: Probability and Statistics Honors (Specifically in versions: 2014 - 2015, 2015 - 2019, 2019 - 2022, 2022 and beyond (current))

Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.

Related Resources

Vetted resources educators can use to teach the concepts and skills in this benchmark.

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.

Type: Formative Assessment

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.

Type: Formative Assessment

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.

Type: Formative Assessment

Algebra Test Scores:

Students are asked to select a histogram for which it would be appropriate to apply the 68-95-99.7 rule.

Type: Formative Assessment

Lesson Plans

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.

Type: Lesson Plan

Texting and Standard Deviation:

This lesson uses texting to teach statistics. In the lesson, students will calculate the mean, median, and standard deviation. They will create a normal distribution using the mean and standard deviation and estimate population percentages. They will construct and interpret dot plots based on the data they collected. Students will also use similarities and differences in shape, center, and spread to determine who is better at texting, boys, or girls.

Type: Lesson Plan

Close to the Crossbar with Standard Deviation:

The lesson will connect student's prior knowledge of measures of central tendency to standard deviation and variance. Students will learn how to calculate and analyze variance and standard deviation. With a partner, students will collect data from kicking a ball into a goal mark. Students will collect data and find the mean, then calculate standard deviation and variance, and compare the data between boys and girls. They will analyze the data distribution in terms of how many students are within certain numbers of standard deviations from the mean.

Type: Lesson Plan

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.

Type: Lesson Plan

Plane Statistics:

This lesson starts with an activity to gather data using paper airplanes then progresses to using appropriate statistics to compare the center and spread of the data. Box plots are used in this application lesson of concepts and skills previously acquired.

Type: Lesson Plan

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.

Type: Lesson Plan

Picturing the Normal World:

This is an introductory lesson on normally distributed data. Students will calculate the standard deviation and use the Empirical Rule.

Type: Lesson Plan

In terms of soccer: Nike or Adidas?:

In this lesson, students calculate and interpret the standard deviation for two data sets. They will measure the air pressure for two types of soccer balls. This lesson can be used as a hands-on activity or completed without measuring using sample data.

Type: Lesson Plan

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.

Type: Lesson Plan

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?

Type: Lesson Plan

The Cereal Prize Estimation:

How many boxes of cereal would you have to purchase to win all six prizes?

This lesson uses class data collected through simulations to allow students to answer this question. Students simulate purchasing cereal boxes and create a t-confidence interval with their data to determine how many boxes they can expect to buy.

Type: Lesson Plan

Sweet Statistics - A Candy Journey:

Students will sort pieces of candy by color and then calculate statistical information such as mean, median, mode, interquartile range, and standard deviation. They will also create an Excel spreadsheet with the candy data to generate pie charts and column charts. Finally, they will compare experimental data to theoretical data and explain the differences between the two. This is intended to be an exercise for an Algebra 1 class. Students will need at least 2 class periods to sort their candy, make the statistical calculations, and create the charts in Excel.

Type: Lesson Plan

The Debate: Who is a Better Baller?:

In this activity the students will use NBA statistics on Lebron James and Tim Duncan who were key players in the 2014 NBA Finals, to calculate, compare, and discuss mean, median, interquartile range, variance, and standard deviation. They will also construct and discuss box plots.

Type: Lesson Plan

Perspectives Video: Expert

Statistical Inferences and Confidence Intervals :

Florida State University Counseling Psychologist discusses how he uses confidence intervals to make inferences on college students' experiences on campus based on a sample of students.

Type: Perspectives Video: Expert

Perspectives Video: Professional/Enthusiast

Nestle Waters & Statistical Analysis:

Hydrogeologist from Nestle Waters discusses the importance of statistical tests in monitoring sustainability and in maintaining consistent water quality in bottled water.

Type: Perspectives Video: Professional/Enthusiast

Perspectives Video: Teaching Idea

Smile Statistics:

This quantitative measurement and statistics activity will allow you to save face.

Type: Perspectives Video: Teaching Idea

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.

Type: Problem-Solving Task

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.

Type: Problem-Solving Task

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.

Type: Problem-Solving Task

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.

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.

Student Resources

Vetted resources students can use to learn the concepts and skills in this benchmark.

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.

Type: Problem-Solving Task

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.

Type: Problem-Solving Task

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.

Type: Problem-Solving Task

Parent Resources

Vetted resources caregivers can use to help students learn the concepts and skills in this benchmark.

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.

Type: Problem-Solving Task

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.

Type: Problem-Solving Task

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.

Type: Problem-Solving Task