This lesson unit is intended to help you assess how well students are able to: Calculate the mean, median, mode, and range from a frequency chart; and to use a frequency chart to describe a possible data set, given information on the mean, median, mode, and range.
The students will use ACC basketball statistics to practice the process of converting fractions to decimals then to percents and will learn how to create and edit a spreadsheet. They will then use this spreadsheet to analyze their data. This unit is done during the basketball season which takes approximately 15 weeks from the middle of November to the middle of March. Teachers must have Clarisworks to open the sample spreadsheet in the lesson, but may recreate it in another spreadsheet program.
- Statistics and Probability
- Material Type:
- Lesson Plan
- University of North Carolina at Chapel Hill School of Education
- Provider Set:
- LEARN NC Lesson Plans
- Susan Dougherty
- Date Added:
Lesson OverviewStudents complete a card sort that requires them to match sets of statistics with the corresponding line plots.Students match cards with simple line plots to the corresponding card with measures of center. Some cards include mode, mean, median, and range, and some have one or two measures missing. Students discuss how they determined which cards would match.Key ConceptsTo complete the card sort in this lesson efficiently, students must be able to relate statistical measures with line plots. If they start with the measures that are easy to see, they can narrow down the possible matches.The mode is the easiest measure to see immediately. It is simply the number with the tallest column of dots.The range can be found easily by subtracting the least value in the plot from the greatest.The median can be found fairly quickly by counting to the middle dot or by pairing dots on the ends until reaching the middle.The mean must be calculated by adding data values and dividing.Goals and Learning ObjectivesApply knowledge of measures of center and range to solve problems.Discuss and review strategy choices when problem solving.
Students will apply what they have learned in previous lessons to analyze and draw conclusions about a set of data. They will also justify their thinking based on what they know about the measures (e.g., I know the mean is a good number to use to describe what is typical because the range is narrow and so the MAD is low.).Students analyze one of the data sets about the characteristics of sixth grade students that was collected by the class in Lesson 2. Students construct line plots and calculate measures of center and spread in order to further their understanding of the characteristics of a typical sixth grade student.Key ConceptsNo new mathematical ideas are introduced in this lesson. Instead, students apply the skills they have acquired in previous lessons to analyze a data set for one attribute of a sixth grade student. Students make a line plot of the data and find the mean, median, range, MAD, and outliers. They use these results to determine a typical value for their data.Goals and Learning ObjectivesDescribe an attribute of a typical sixth grade student using line plots and measures of center (mean and median) and spread (range and MAD).Justify thinking about which measures are good descriptors of the data set.
In this module, students move from simply representing data into analysis of data. Students begin to think and reason statistically, first by recognizing a statistical question as one that can be answered by collecting data. Students learn that the data collected to answer a statistical question has a distribution that is often summarized in terms of center, variability, and shape. Throughout the module, students see and represent data distributions using dot plots and histograms. They study quantitative ways to summarize numerical data sets in relation to their context and to the shape of the distribution. As the module ends, students synthesize what they have learned as they connect the graphical, verbal, and numerical summaries to each other within situational contexts, culminating with a major project.
In this activity, students reinforce their understanding of compound machines by building a catapult. This compound machine consists of a lever and a wheel-and-axel. Catapults have been designed by engineers for a variety of purposes from lifting boulders into the air for warfare to human beings for entertainment; the projectiles in this activity are grapes for a magic act. Given the building materials, students design and build their catapult to launch a grape a certain distance.
Students critique and improve their work on the Self Check from Lesson 13.Key ConceptsMeasures of spread (five-number summary) show characteristics of the data. It is possible to generate an appropriate data set with this information.Goals and Learning ObjectivesApply knowledge of statistics to solve problems.Identify the five-number summary, and understand measures of center and use their properties to solve problems.Track and review choice of strategy when problem solving.
In this lesson, students are given criteria about measures of center, and they must create line plots for data that meet the criteria. Students also explore the effect on the median and the mean when values are added to a data set.Students use a tool that shows a line plot where measures of center are shown. Students manipulate the graph and observe how the measures are affected. Students explore how well each measure describes the data and discover that the mean is affected more by extreme values than the mode or median. The mathematical definitions for measures of center and spread are formalized.Key ConceptsStudents use the Line Plot with Stats interactive to develop a greater understanding of the measures of center. Here are a few of the things students may discover:The mean and the median do not have to be data points.The mean is affected by extreme values, while the median is not.Adding values above the mean increases the mean. Adding values below the mean decreases the mean.You can add values above and below the mean without changing the mean, as long as those points are “balanced.”Adding values above the median may or may not increase the median. Adding values below the median may or may not decrease the median.Adding equal numbers of points above and below the median does not change the median.The measures of center can be related in any number of ways. For example, the mean can be greater than the median, the median can be greater than the mean, and the mode can be greater than or less than either of these measures.Note: In other courses, students will learn that a set of data may have more than one mode. That will not be the case in this lesson.Goals and Learning ObjectivesExplore how changing the data in a line plot affects the measures of center (mean, median).Understand that the mean is affected by outliers more than the median is.Create line plots that fit criteria for given measures of center.
Students use the Box Plot interactive, which allows them to create line plots and see the corresponding box plots. They use this tool to create data sets with box plots that satisfy given criteria.Students investigate how the box plot changes as the data points in the line plot are moved. Students can manipulate data points to change aspects of the box plot and to see how the line plot changes. Students create box plots that fit certain criteria.Key ConceptsThis lesson focuses on the connection between a data set and its box plot. It reinforces the idea that a box plot shows the spread of a data set, but not the individual data points.Students will observe the following similarities and differences between line plots and box plots:Line plots allow us to see and count individual values, while box plots do not.Line plots allow us to find the mean and the mode of a set of data, while box plots do not.Box plots are useful for very large data sets, while line plots are not.Box plots give us a better picture of how the values in a data set are distributed than line plots do, and they allow us to see measures of spread easily.Goals and Learning ObjectivesExperiment with different line plots to see the effect on the corresponding box plots.Create data sets with box plots that satisfy different criteria.Compare and contrast line plots and box plots.
Distributions and Variability
Type of Unit: Project
Students should be able to:
Represent and interpret data using a line plot.
Understand other visual representations of data.
Students begin the unit by discussing what constitutes a statistical question. In order to answer statistical questions, data must be gathered in a consistent and accurate manner and then analyzed using appropriate tools.
Students learn different tools for analyzing data, including:
Measures of center: mean (average), median, mode
Measures of spread: mean absolute deviation, lower and upper extremes, lower and upper quartile, interquartile range
Visual representations: line plot, box plot, histogram
These tools are compared and contrasted to better understand the benefits and limitations of each. Analyzing different data sets using these tools will develop an understanding for which ones are the most appropriate to interpret the given data.
To demonstrate their understanding of the concepts, students will work on a project for the duration of the unit. The project will involve identifying an appropriate statistical question, collecting data, analyzing data, and presenting the results. It will serve as the final assessment.
Students make a box plot for their typical-sixth-grader data from Lesson 7 and write a summary of what the plot shows.Using the line plot from Lesson 4, students construct a box plot. Students learn how to calculate the five-number summary and interquartile range (IQR). Students apply this knowledge to the data used in Lesson 7 and describe the data in terms of the box plot. Class discussion focuses on comparing the two graphs and what they show for the sets of data.Key ConceptsA box-and-whisker plot, or box plot, shows the spread of a set of data. It shows five key measures, called the five-number summary.Lower extreme: The smallest value in the data setLower quartile: The middle of the lower half of the data, and the value that 25% of the data fall belowMedian: The middle of the data setUpper quartile: The middle of the upper half of the data, and the value that 25% of the data are aboveUpper extreme: The greatest value in the data setThis diagram shows how these values relate to the parts of a box plot.The length of the box represents the interquartile range (IQR), which is the difference between the lower and upper quartile.A box plot divides the data into four equal parts. One quarter of the data is represented by the left whisker, two quarters by each half of the box, and one quarter by the right whisker. If one of these parts is long, the data in that quarter are spread out. If one of these quarters is short, the data in that quarter are clustered together.Goals and Learning ObjectivesLearn how to construct box plots, another tool to describe data.Learn about the five-number summary, interquartile range, and how they are related to box plots.Compare a line plot and box plot for the same set of data.