Standard 5: Determine methods of data collection and make inferences from collected data.

General Information
Number: MA.912.DP.5
Title: Determine methods of data collection and make inferences from collected data.
Type: Standard
Subject: Mathematics (B.E.S.T.)
Grade: 912
Strand: Data Analysis and Probability

Related Benchmarks

This cluster includes the following benchmarks.

Related Access Points

This cluster includes the following access points.

Access Points

MA.912.DP.5.AP.11
Given a graph representing data, select whether the graph is misleading or not (i.e., scale on x and y axis not consistent, circle graph does not add up to 100%; missing title or title doesn’t represent data; or bar widths on bar graph are inconsistent).

Related Resources

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

Lesson Plans

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

Comparing Standard Deviation:

Students will predict and compare standard deviation from a dot plot. Each data set is very different, with a small variation vs. a larger variation. The students are asked to interpret the standard deviation after calculating the range and mean of the each data set.

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

Bowling for Box Plots:

Students will learn about the effects of an outlier and interpret differences in shape, center, and spread using a bowling activity to gather data. The students will learn to score their games, report their scores, and collectively measure trends and spread by collaborating to create a box plot. They will analyze and compare box plots, and determine how much of an effect an extreme score (outlier) can have on the overall box plot of the data.

Type: Lesson Plan

What's My Grade?:

"What's My Grade" is a lesson that will focus on a sample student's grades to demonstrate how a final grade is calculated as well as explore possible future grades. Students will create the distributions of each grade category using histograms. They will also analyze grades using mean and standard deviation. Students will use statistics to determine data distribution while comparing the center and spread of two or more different data sets.

Type: Lesson Plan

How tall is an 8th grader?:

Ever wonder about the differences in heights between students in grade 8? In this lesson, students will use data they collect to create and analyze multiple box plots using 5-number summaries. Students will make inferences about how height and another category may or may not be related.

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

The Distance a Coin Will Travel:

This lesson is a hands-on activity that will allow students to collect and display data about how far different coins will travel. The data collected is then used to construct double dot plots and double box plots. This activity helps to facilitate the statistical implications of data collection and the application of central tendency and variability in data collection.

Type: Lesson Plan

Which is Better? Using Data to Make Choices:

Students use technology to analyze measures of center and variability in data. Data displays such as box plots, line plots, and histograms are used. The effects of outliers are taken into consideration when drawing conclusions. Students will cite evidence from the data to support their conclusions.

Type: Lesson Plan

How many licks does it take to get to the center?:

Students will create different displays, line plots, histograms, and box plots from data collected about types of lollipops. The data will be analyzed and compared. Students will determine "Which lollipop takes the fewest number of licks to get to the center: a Tootsie Pop, a Blow Pop, or a Dum Dum?"

Type: Lesson Plan

Birthday Party Decisions:

Students will create and compare four different boxplots to determine the best location for a birthday party.

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

Comparing Data Using Box Plots:

Students will use box plots to compare two or more sets of data. They will analyze data in context by comparing the box plots of two or more data sets.

Type: Lesson Plan

Digging the Plots:

Students construct box plots and use the measure(s) of center and variability to make comparisons, interpret results, and draw conclusions about two populations.

Type: Lesson Plan

Centers, Spreads, and Outliers:

The students will compare the effects of outliers on measures of center and spread within dot plots and box plots.

Type: Lesson Plan

Should Statistics be Shapely?:

Students will Interpret differences in shape, center, and spread of a variety of data displays, accounting for possible effects of extreme data points.

Students will create a Human Box Plot using their data to master the standard and learning objectives, then complete interactive notes with the classroom teacher, a formative assessment, and later a summative assessment to show mastery.

Type: Lesson Plan

Show Me the Money:

Students will create a statistical question and collect and analyze data using relative frequency tables. They will present their argument in hopes of earning a cash prize for their philanthropy. An iterative process of critique and refinement will take place. A student packet is included that guides all parts of the lesson.

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

Changing World Oceans - An Ocean Acidification Simulation:

This 5-day lesson introduces students to the phenomenon of ocean acidification, including processes involved and the importance it has on Earth ecosystems. It focuses on the atmosphere / hydrosphere interaction with respect to carbon dioxide. The lesson progresses from the introductory first day where student preconceptions and misconceptions are identified and addressed in an introductory lesson. The lab on the second day can be accomplished using non-specialized, inexpensive equipment or more sophisticated probeware. Day 3 is for data analysis and reflecting on the lab results and building process diagrams, and days 4 and 5 are time for writing the lab report.

Type: Lesson Plan

Exploring Box plots:

This lesson involves real-world data situations. Students will use the data to create, explore, and compare the key components of a box plot.

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

Who's Better?--Using Data to Determine:

This lesson is intended for use after students are able to construct data plots (histograms, line plots, box plots). Students are tasked with not only constructing data plots, but also matching data plots to data sets. In the summative assessment, students are given two data sets and asked to select which of three data plots (histogram, line plot, or box plot) would best be used to compare the data. After choosing and constructing their plot, students are then tasked with forming a conclusion based on the plots they have constructed.

Type: Lesson Plan

Is It a Guess or Statistics?:

This lesson teaches random sampling which leads to making inferences about a larger group or population. Students will determine the best measure of center to use for a data set. Students will collect data, select a data display and then analyze the data.

Type: Lesson Plan

Advantages and Disadvantages of Dot Plots, Histograms, and Box Plots:

Students will compare the advantages and disadvantages of dot plots, histograms, and box plots. During this lesson, students will review the statistical process and learn the characteristics of a statistical question; whether it be numerical or categorical. Students will apply the information learned in a project that involves real-world issues and make an analysis based on the data collected.

Type: Lesson Plan

Inferences:

This lesson shows students how to conduct a survey and display their results. The lesson takes the students through:

  1. What is a statistical question?
  2. General population versus sample population.
  3. What is a hypothesis?
  4. What is a survey?
  5. How to make inferences.

Type: Lesson Plan

To The Limit:

"To The Limit" MEA has students identify several factors that can affect a population’s growth. Students will examine photos to list limiting factors and discuss their impact on populations. As a group they will develop a solution to minimize the impact of pollution on fish population.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.

Type: Lesson Plan

5K and No More - Producing Data:

Can your school use $5000? What school doesn't?! Well, the money is available, but the student body must decide how the money will be spent!

5K and No More - Producing Data will enable students to fantasize about what they would do to improve their school if allowed to answer the question, "How would $5000 best be spent at your school?" The activity begins with students distinguishing the differences between a sample survey, an experiment, and an observational study through a pre-activity. After this, the students are given five (5) scenarios in which they must discuss the pros and cons of each. In life we want things to be fair, so students must constantly think about bias. The company in this MEA desires the most efficient and effective way to collect information from the students without having to talk to everyone ... who has that kind of time!

Now, just when the students have found the most efficient and effective way to get students to share their thoughts on where the money should go, more information is revealed about the High School. How do we account for the brains and the brawn, the perfect attendee and the most missed days, or for the goth or skater?

Your Savvy Statisticians in the making will figure it out and tell you ALL about it.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. MEAs resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. Students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem while considering constraints and tradeoffs. Students integrate their ELA skills into MEAs as they are asked to clearly document their thought processes. MEAs follow a problem-based, student-centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. To learn more about MEAs visit: https://www.cpalms.org/cpalms/mea.aspx

Type: Lesson Plan

Generating Multiple Samples to Gauge Variation:

Students explore variation in random samples and use random samples to make generalizations about the population.

Type: Lesson Plan

How Fast Do Objects Fall?:

Students will investigate falling objects with very low air friction.

Type: Lesson Plan

Perspectives Video: Experts

Birdsong Series: Statistical Analysis of Birdsong:

<p>Wei&nbsp;Wu discusses his statistical contributions to the Birdsong project which help to quantify&nbsp;the differences in the changes of the zebra finch's song.</p>

Type: Perspectives Video: Expert

Birdsong Series: Mathematically Modeling Birdsong:

Richard Bertram discusses his mathematical modeling contribution to the Birdsong project that helps the progress of neuron and ion channel research.

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Expert

Birdsong Series: STEM Team Collaboration :

<p>Researchers Frank Johnson, Richard Bertram,&nbsp;Wei&nbsp;Wu, and Rick&nbsp;Hyson&nbsp;explore the necessity of scientific and mathematical collaboration in modern neuroscience, as it relates to their NSF research on birdsong.</p>

Type: Perspectives Video: Expert

fMRI, Phantom Limb PainĀ and Statistical Noise:

<p>Jens Foell&nbsp;discusses how statistical noise reduction is used in fMRI&nbsp;brain imaging to be able to determine which specifics parts of the brain are related to certain activities and how this relates to patients that suffer from phantom limb pain.</p>

Type: Perspectives Video: Expert

How Math Models Help Insurance Companies After a Hurricane Hits:

Hurricanes can hit at any time! How do insurance companies use math and weather data to help to restore the community?

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Expert

Probabilistic Weather Modeling:

Meteorologist from Risk Management discusses the use of probability in predicting hurricane tracks.

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Expert

PTSD: Correlation vs Causation:

Jens Foell discusses the link between correlation and causation in PTSD patients.

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Expert

Statistical Inferences and Confidence Intervals :

<p>Florida State University Counseling Psychologist&nbsp;discusses how he uses confidence intervals to make inferences on college students' experiences on campus based on a sample of students.</p>

Type: Perspectives Video: Expert

MicroGravity Sensors & Statistics:

Statistical analysis played an essential role in using microgravity sensors to determine location of caves in Wakulla County.

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Expert

Let's Make a Math Deal:

Should I keep my choice or switch? Learn more about the origins and probability behind the Monty Hall door picking dilemma and how Game Theory and strategy effect the probability.

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Expert

History of Probability and the Problem of Points:

What was the first question that started probability theory?

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Expert

Hurricanes & Strong Deep Ocean Currents:

COAPS oceanographer Steve Morey describes how math is used to help research hurricanes and strong deep ocean currents that could effect deep water oil rigs.

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Expert

Carbon Foam and Geometry:

<p>Carbon can take many forms, including foam! Learn more about how geometry and the Monte Carlo Method is important in understanding it.</p>

Type: Perspectives Video: Expert

Mathematical Modeling of El NiƱo :

<p>Hear how mathematics helped shape Dr. James O'Brien's groundbreaking research in ocean modeling of El Ni&ntilde;o.</p>

Type: Perspectives Video: Expert

Improving Hurricane Modeling by Reducing Systematic Errors:

<p>This FSU professor discusses the limitations and need for improvement to models used to forecast hurricanes.</p>

Type: Perspectives Video: Expert

Perspectives Video: Professional/Enthusiasts

Nestle Waters & Statistical Analysis:

<p>Hydrogeologist&nbsp;from Nestle Waters discusses the importance&nbsp;of statistical tests in monitoring&nbsp;sustainability and in maintaining consistent&nbsp;water quality in bottled water.</p>

Type: Perspectives Video: Professional/Enthusiast

Fishery Independent vs Dependent Sampling Methods for Fishery Management:

<p>NOAA&nbsp;Scientist Doug Devries discusses the differences between fishery independent surveys and fishery independent surveys. &nbsp;Discussion&nbsp;includes trap sampling as well as camera sampling. Using&nbsp;graphs to show changes in population of red snapper.</p>

Type: Perspectives Video: Professional/Enthusiast

Sample Size and Shark Research:

<p>Deep sea shark researcher, Chip Cotton, discusses the need for a Power Analysis to determine the critical sample size in order to make inferences on how oil spills affect shark populations.</p>

Type: Perspectives Video: Professional/Enthusiast

Camera versus Trap Sampling: Improving how NOAA Samples Fish :

<p>Underwater sampling with cameras has made fishery management more accurate for NOAA&nbsp;scientists.</p>

Type: Perspectives Video: Professional/Enthusiast

Linear Regression for Analysis of Sea Anemone Data:

<p>Will Ryan describes how linear regression models contribute towards his research on sea anemones.</p>

Type: Perspectives Video: Professional/Enthusiast

Hydrologic Modeling and Reservoir Simulation:

Dr. Tom Van Lent and Rajendra Paudel describe how modeling and simulation of water reservoirs are used to inform decisions about regulation of water flow in the Everglades.

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Professional/Enthusiast

Modeling the Everglades with Mathematics:

Dr. Tom Van Lent and Rajendra Paudel describe how hydrologic modeling is used to evaluate environmental conditions in the Everglades.

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Professional/Enthusiast

Sampling Strategies for Ecology Research in the Intertidal Zone:

<p>Will Ryan describes methods for collecting multiple random samples of anemones in coastal marine environments.</p>

Type: Perspectives Video: Professional/Enthusiast

Hurricane Dennis & Failed Math Models:

What happens when math models go wrong in forecasting hurricanes?

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Professional/Enthusiast

Making Inferences about Wetland Population Sizes:

<p>This ecologist from the Coastal Plains Institute discusses sampling techniques that are used to gather data to make statistical inferences about amphibian populations in the wetlands of the Apalachicola National Forest.</p>

Type: Perspectives Video: Professional/Enthusiast

Sampling Amphibian Populations to Study Human Impact on Wetlands:

<p>Ecologist Rebecca Means discusses the use of statistical sampling and comparative studies in field biology.</p>

Type: Perspectives Video: Professional/Enthusiast

How to Build a Research Study on Education:

<p>This researcher explains common methods behind randomized studies in the social sciences, specifically in education.</p>

Type: Perspectives Video: Professional/Enthusiast

Statistical Analysis of a Randomized Study:

<p>This education researcher uses measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations.</p>

Type: Perspectives Video: Professional/Enthusiast

Population Sampling and Beekeeping:

<p>This buzzworthy video features statistics, sampling, and how scientists make inferences about populations.</p>

Type: Perspectives Video: Professional/Enthusiast

Problem-Solving Tasks

Sarah, the Chimpanzee:

The purpose of this task is to give students experience in using simulation to determine if observed results are consistent with a given model (in this case, the "just guessing" model).

Type: Problem-Solving Task

Why Randomize?:

This task requires students to estimate the mean (average) area of the population of 100 rectangles using the average area of a sample of 5 rectangles. Students are asked to make one estimate using a judgement sample and another using a random sample of the population. Finally, students are asked to consider bias in sampling methods.

Type: Problem-Solving Task

Strict Parents:

This task challenges students to describe parameter of interest for the given context, and design a sample survey.

Type: Problem-Solving Task

Musical Preferences:

This problem solving task asks students to make deductions about the kind of music students enjoy by examining data in a two-way table.

Type: Problem-Solving Task

School Advisory Panel:

Students are asked to choose the best sampling method for choosing the new School Advisory Panel.

Type: Problem-Solving Task

Block Scheduling:

In this task, output is given from a computer-generated simulation, generating size-100 samples of data from an assumed school population of 2000 students under hypotheses about the true distribution of yes/no voters. Students are asked to draw conclusions about reliability using simulated distributions.

Type: Problem-Solving Task

Words and Music II:

The purpose of this task is to assess (1) ability to distinguish between an observational study and an experiment and (2) understanding of the role of random assignment to experimental groups in an experiment.

Type: Problem-Solving Task

Estimating the Mean State Area:

The task is designed to show that random samples produce distributions of sample means that center at the population mean, and that the variation in the sample means will decrease noticeably as the sample size increases.

Type: Problem-Solving Task

Teaching Idea

An Ecological Field Study with Statistical Analysis of Two Populations:

Students will design an investigation that compares a characteristic of two populations of the same species. Students will collect data in the field and analyze the data using descriptive statistics.

Type: Teaching Idea

Text Resources

Sample Size Calculation:

This informational text resource is intended to support reading in the content area. This article describes the important process used when setting up trials for statistical investigation. The article explains each parameter that is needed to calculate the sample size, then provides examples and illustrates the process. This article will enhance an upper level math course's study of statistics after significance levels and basic inferential statistics concepts have been taught.

Type: Text Resource

Understanding Uncertainty: What Was the Probability of Obama Winning?:

This informational text resource is intended to support reading in the content area. The article examines various factors that changed the uncertainty of whether Barack Obama would win the 2008 election. Specifically,the article discusses probability, the science of quantifying uncertainty. The article questions common methods for assessing probability where symmetrical outcomes are assumed. Finally, the author explains how to use past evidence to assess the chances of future events.

Type: Text Resource

How to Win at Rock-Paper-Scissors:

This informational text resource is intended to support reading in the content area. This article describes a new study about the game rock-paper-scissors. The study reveals that people do not play randomly; there are patterns and hidden psychology players frequently use. Understanding these potential moves can help a player increase their winning edge. As part of interpreting the results of the study, the article references the Nash equilibrium and the "win-stay lose-shift" strategy.

Type: Text Resource

Student Resources

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

Perspectives Video: Expert

MicroGravity Sensors & Statistics:

Statistical analysis played an essential role in using microgravity sensors to determine location of caves in Wakulla County.

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Expert

Perspectives Video: Professional/Enthusiast

Population Sampling and Beekeeping:

<p>This buzzworthy video features statistics, sampling, and how scientists make inferences about populations.</p>

Type: Perspectives Video: Professional/Enthusiast

Problem-Solving Tasks

Musical Preferences:

This problem solving task asks students to make deductions about the kind of music students enjoy by examining data in a two-way table.

Type: Problem-Solving Task

School Advisory Panel:

Students are asked to choose the best sampling method for choosing the new School Advisory Panel.

Type: Problem-Solving Task

Words and Music II:

The purpose of this task is to assess (1) ability to distinguish between an observational study and an experiment and (2) understanding of the role of random assignment to experimental groups in an experiment.

Type: Problem-Solving Task

Parent Resources

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

Perspectives Video: Professional/Enthusiast

Population Sampling and Beekeeping:

<p>This buzzworthy video features statistics, sampling, and how scientists make inferences about populations.</p>

Type: Perspectives Video: Professional/Enthusiast

Problem-Solving Tasks

Musical Preferences:

This problem solving task asks students to make deductions about the kind of music students enjoy by examining data in a two-way table.

Type: Problem-Solving Task

School Advisory Panel:

Students are asked to choose the best sampling method for choosing the new School Advisory Panel.

Type: Problem-Solving Task

Words and Music II:

The purpose of this task is to assess (1) ability to distinguish between an observational study and an experiment and (2) understanding of the role of random assignment to experimental groups in an experiment.

Type: Problem-Solving Task