Standard 1: Develop an understanding of statistics and determine measures of center and measures of variability. Summarize statistical distributions graphically and numerically.

Students are asked to construct a box plot corresponding to a given set of data.

Type: Formative Assessment

Students are asked to calculate measures of center and variability, identify outliers, and interpret the meaning of each in context.

Type: Formative Assessment

Students are given a histogram and are asked to describe the variable under investigation and the number of observations.

Type: Formative Assessment

Students are asked to list measures of variability and explain what they indicate about a set of data.

Type: Formative Assessment

Students are asked to list measures of center and explain what they indicate about a set of data.

Type: Formative Assessment

Students are asked to explain the difference between measures of center and measures of variability.

Type: Formative Assessment

Students are asked to construct a histogram corresponding to a given set of data.

Type: Formative Assessment

Students are asked to determine whether or not questions are statistical and justify their responses.

Type: Formative Assessment

Students are asked to write a statistical question and explain why it is statistical.

Type: Formative Assessment

Students are asked to select the better measure of center and variability to describe each of two distributions of data.

Type: Formative Assessment

Students are asked to describe and compare the centers of two data sets given their dot plots.

Type: Formative Assessment

Students are asked to calculate measures of center and variability, identify extreme values, and interpret the meaning of each in context.

Type: Formative Assessment

Students are asked to describe the distribution of data given in raw form.

Type: Formative Assessment

Students are asked to describe and compare the spread of the distribution of two data sets given their dot plots.

Type: Formative Assessment

Students are asked to describe the shapes of three distributions given their dot plots and to explain the shapes in terms of the context.

Type: Formative Assessment

Using relatable scenarios, this lesson explores the mean and median of a data set and how an outlier affects each measure differently.

Type: Lesson Plan

This lesson explores the use of box plots and the mean absolute deviation to compare two data sets and draw inferences.

Type: Lesson Plan

In this interdisciplinary lesson, students will practice the skill of data collection with a variety of tools and by statistically analyzing the class data sets will begin to understand that error is inherent in all data.

Type: Lesson Plan

This lesson is designed for students to demonstrate their knowledge of box plots.

• Students will need to create four box plots from given data.
• Students will need to analyze the data displayed on the box plots by comparing similarities and differences.
• Students will work with a partner to complete the displays and the follow-up questions.

Type: Lesson Plan

Students will compile the data gathered from measuring their resting heart rates and heart rates after exercising into box plots. Using these displays, they will analyze the data's center, shape, and spread.

Type: Lesson Plan

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" 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

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

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

Students will be asked to obtain data and create a human box plot, which will be analyzed and explained using statistical terms. Students will then understand the differences and advantages to using the box plot, histogram, and dot plot. Students will also practice selecting the most appropriate graphical representation for a set of data.

Type: Lesson Plan

This resource can be used to teach students how to create and compare box plots. After completing this lesson, students should be able to answer questions in both familiar and unfamiliar situations.

Type: Lesson Plan

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

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

Students will create and analyze histograms based on student study time when preparing for the Algebra EOC. Students will be given a set of data and guided notes

Type: Lesson Plan

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

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

Type: Lesson Plan

Students will explore the effects outliers have on the mean and median values using the Major League Baseball (MLB) salary statistics. They will create and compare box plots and analyze measures of center and variability. They will also be given a set of three box plots and asked to identify and compare their measures of center and variablity.

Type: Lesson Plan

This lesson allows students to have a hands-on experience collecting real-world data, creating graphical representations, and analyzing their data. Students will make predictions as to the outcome of the data and compare their predictions to the actual outcome. Students will create and analyze line plots, histograms, and box plots.

Type: Lesson Plan

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

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

Students will collect data, and create box plots. Students will make predictions about which measurement best describes the spread and center of the data. Students will use this information to make predictions.

Type: Lesson Plan

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

For this lesson, students will research the ages of players on two basketball teams. They will find the five-number summary, the mean, and determine if there are outliers in the data set. Two box plots will be created and the measures of center and variation analyzed.

Type: Lesson Plan

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

Type: Lesson Plan

Students will design an investigation to collect and analyze data, determine results, write a justification and make a presentation using U.S. pennies.

Paired student teams will determine the mass of 50 U.S. pennies. Students will also collect other data from each penny such as minted year and observable appearance. Students will be expected to organize/represent their data into tables, histograms and other informational structures appropriate for reporting all data for each penny. Students will be expected to consider the data, determine trends, and research information in order to make a claim that explains trends in data from minted U.S. pennies.

Hopefully, student data reports will support the knowledge that the metallic composition of the penny has changed over the years. Different compositions can have significantly different masses. A sufficiently random selection of hundreds of pennies across the class should allow the students to discover trends in the data to suggest the years in which the composition changed.

Type: Lesson Plan

Students experiment with baking soda and vinegar and use statistics to determine which ratio of ingredients creates the most carbon dioxide. This hands-on activity applies the concepts of plot, center, and spread.

Type: Lesson Plan

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

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

Students will be given data and then plot the data using a graphical method of choice (dot plot, bar graph, box plot, etc.) The students will work in groups and then analyze and summarize the data.

Type: Lesson Plan

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

Students will analyze various real world scenario data sets and create, analyze, and interpret the components of the box plots. Students will use data from morning routines, track times, ages, etc. Lesson includes a PowerPoint, homework, and assessments.

Type: Lesson Plan

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

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

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

Students will create double box plots to compare nutritional data about popular food choices.

Type: Lesson Plan

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

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

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

An introduction lesson on creating and interpreting box plots.

Type: Lesson Plan

The student explores several strategies for selecting a sample population to support making inferences about the population.

Type: Lesson Plan

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

Type: Lesson Plan

Using relatable scenarios, this lesson explores the mean and median of a data set and how an outlier affects each measure differently.

Type: Lesson Plan

Students will review measures of central tendency and practice selecting the best measure with real-world categorical data. This relatable scenario about ranking the characteristics considered when purchasing a pair of sneakers, is used to finally answer the age-old question of "When will I ever use this?".

Type: Lesson Plan

This lesson explores the creation of box plots to compare two data sets and draw inferences.

Type: Lesson Plan

Learn how math models can show why social distancing during a epidemic or pandemic is important in this interactive tutorial.

Type: Original Student Tutorial

Learn how to interpret histograms to analyze data, and help an inventor predict the range of a catapult in part 2 of this interactive tutorial series. More specifically, you'll learn to describe the shape and spread of data distributions.

Click HERE to open part 1.

Type: Original Student Tutorial

Learn how to create a histogram to display continuous data from projectiles launched by a catapult in this interactive tutorial. 

This is part 1 in a 2-part series. Click HERE to open part 2.

Type: Original Student Tutorial

Learn how to make and interpret boxplots in this pet-themed, interactive tutorial.

Type: Original Student Tutorial

Discover how to calculate and interpret the mean, median, mode and range of data sets from the zoo in this interactive tutorial.

Type: Original Student Tutorial

Entrepreneur and meteorologist Mark Powell discusses the need for statistics in his mathematical modeling program to help better understand hurricanes.

Type: Perspectives Video: Expert

NOAA Fishery management relies on histograms to show patterns and trends over time of fishery data.

Type: Perspectives Video: Expert

Ecologist, Rebecca Means, describes the process of determining remote locations in the USA and developing quantitative questions that are appropriate.

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Professional/Enthusiast

What does it mean to be normally distributed?  What do oceanographers do when the collected data is not normally distributed? 

Type: Perspectives Video: Professional/Enthusiast

This marine biologist discusses her use of graphical representations to help determine the most cost-effective management strategies for sea turtle conservation.

Type: Perspectives Video: Professional/Enthusiast

Unlock an effective teaching strategy for teaching median, mode, and range in this Teacher Perspectives Video for educators.

Type: Perspectives Video: Teaching Idea

This activity will send your measurement lab to new distances.

Type: Perspectives Video: Teaching Idea

This problem could be used as an introductory lesson to introduce group comparisons and to engage students in a question they may find amusing and interesting.

Type: Problem-Solving Task

Students are given a context and a dotplot and are asked a number of questions regarding shape, center, and spread of the data.

Type: Problem-Solving Task

Students are given a context and a series of questions and are asked to identify whether each question is statistical and to provide their reasoning. Students are asked to compose an original statistical question for the given context.

Type: Problem-Solving Task

Using the information provided, create an appropriate graphical display and answer the questions regarding shape, center and variability.

Type: Problem-Solving Task

This activity is a statistical analysis of recorded measurements of a single value - in this case, a partially filled graduated cylinder.

Type: Teaching Idea

Students will measure the mass of one nickel 10 times on a digital scale precise to milligrams. The results will be statistically analyzed to find the error and uncertainty of the scale.

Type: Teaching Idea

Students communicate mathematical ideas and visually represent ideas by constructing charts, graphs, and scale drawings based on information cards about various marine animals.

Type: Teaching Idea

Although a sheet of paper is much thinner than the divisions of a ruler, we can make indirect measurements of the paper's thickness.

Type: Teaching Idea

Students will predict how high they can jump and then compare the height of their jumps to how high a rockhopper penguin can jump out of the water. They will practice mathematical skills for determining averages.

Type: Teaching Idea

This article is intended to support reading in the content area. The text investigates whether the number of large magnitude earthquakes has significantly increased. The article explores the challenge of trying to determine why the amount and intensity of earthquakes can vary across time. The text also briefly explores the recent rise in man-made earthquakes.

Type: Text Resource

In this video, you will practice describing the shape of distributions as skewed left, skewed right, or symmetrical.

Type: Tutorial

The focus of this video is to help you understand the core concepts of arithmetic mean, median, and mode.

Type: Tutorial

This video shows how to find the value of a missing piece of data if you know the mean of the data set.

Type: Tutorial

This video demonstrates how to construct a box plot, formerly known as a box and whisker plot.

Type: Tutorial

Students will interpret data presented in a box plot.  

Type: Tutorial

Learn how to create histograms, which summarize data by sorting it into groups.

Type: Tutorial

Discover what makes a question a "statistical question."

Type: Tutorial

A time-lapse video showing differential growth rates for touch-treated seedlings and control seedlings. This would be appropriate for lessons about plant growth responses to environmental stress and graphing growth rate. Plants were grown in a vermiculite soilless medium with calcium-enhanced water. No other minerals or nutrients were used. Plants were grown in a dark room with specially-filtered green light. The plants did not grow by cellular reproduction but only by expansion of existing cells in the hypocotyl region below the 'hook'.
Video contains three plants in total. The first two plants to emerge from the vermiculite medium are the control (right) and treatment (left) plants. A third plant emerges in front of these two but is removed at the time of treatment and is not relevant except to help indicate when treatment was applied (watch for when it disappears). When that plant disappears, the slowed growth rate of the treatment plant is apparent.
Treatment included a gentle flexing of the hypocotyl region of the treatment seedling for approximately 5 seconds. A rubber glove was used at this time to avoid an contamination of the plant tissue.
Some video players allow users to 'scrub' the playback back and forth. This would help teachers or students isolate particular times (as indicated by the watch) and particular measurements (as indicated by the cm scale). A graph could be constructed by first creating a data table and then plotting the data points from the table. Multiple measurements from the video could be taken to create an accurate graph of the plants' growth rates (treatment vs control).
Instructions for graphing usage:
The scale in the video is in centimeters (one cm increments). Students could observe the initial time on the watch in the video and use that observation to represent time (t) = 0. For that value, a mark could be made to indicate the height of the seedlings. As they advance and pause the video repeatedly, the students would mark the time (+2.5 hours for example) and mark the related seedling heights. It is not necessary to advance the video at any regular interval but is necessary to mark the time and related heights as accurately as possible. Students may use different time values and would thus have different data sets but should find that their graphs are very similar. (Good opportunity to collect data from real research and create their own data sets) It is advised that the students collect multiple data points around the time where the seedling growth slows in response to touch to more accurately collect information around that growth rate slowing event. The resulting graph should have an initial growth rate slope, a flatter slope after stress treatment, and a return to approximately the same slope as seen pre-treatment. More data points should yield a more thorough view of this. This would be a good point to discuss. Students can use some of their data points to calculate approximate pre-treatment, immediate post-treatment, and late post-treatment slopes for both the control and treatment seedlings.
This video was created by the submitter and is original content.
Full screen playback should be an option for most video players. Video quality may appear degraded with a larger image but this may aid viewing the watch and scale for data collection.

Type: Video/Audio/Animation