Unit 7: Statistics
Students investigate how to use sampling to make inferences about larger populations of interest, engaging in hands-on activities to select random samples and to compare samples of different sizes.
In Unit 7, seventh-grade students investigate how they can use sampling to make inferences about larger populations of interest. They begin the unit by understanding that random sampling tends to produce the most representative and “fair” samples and that the size of the sample can make a difference in the accuracy of predictions and the variability of results. Students engage in hands-on activities to select random samples and to compare samples of different sizes. Students also calculate measures of center and variability of samples, most notably, the mean and the mean absolute deviation, or MAD, and use these measures to compare across different populations (MP.2). Throughout the unit, students reason about data, make connections, and defend their reasoning by constructing arguments (MP.3). Students also re-engage in the major work of the grade, particularly their work with ratios and proportions, when they use proportional reasoning to estimate population characteristics based on sample statistics.
In sixth grade, students began their study of statistics by understanding what makes a statistical question. They studied shapes of distributions of data and calculated measures of center and spread. Students made connections between the data and the contexts they represented, ensuring the numerical aspects of statistics were not separated from the statistical question that drove the analysis. All of these understandings will support seventh-grade students in their work in this unit.
In eighth grade, students will shift to study patterns of association in bivariate data. They will collect data to represent two categorical variables and analyze the results to determine if there are associations or tendencies between the variables. Later in high school, students will delve deeply into statistics and, using their understanding of mean and MAD, they will use mean and standard deviation to fit data to normal distributions.
Note: In the CCSSM, the concept of MAD is first introduced in sixth grade. In the Massachusetts Frameworks, MAD is first introduced in seventh grade. This unit follows the MA Frameworks and therefore assumes that students have not had prior experience with MAD.
Pacing: 11 instructional days (9 lessons, 1 flex day, 1 assessment day)
For guidance on adjusting the pacing for the 2021-2022 school year, see our 7th Grade Scope and Sequence Recommended Adjustments.
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This assessment accompanies Unit 7 and should be
given on the suggested assessment day or after completing the
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Suggestions for how to prepare to teach this unit
The central mathematical concepts that students will come to understand in this unit
Terms and notation that students learn or use in the unit
measure of center
mean absolute deviation (mad)
To see all the vocabulary for this course, view our 7th Grade Vocabulary Glossary.
The materials, representations, and tools teachers and students will need for this unit
To see all the materials needed for this course, view our 7th Grade Course Material Overview.
Topic A: Understanding Populations and Samples
Understand and identify populations and sample populations for statistical questions.
Describe sampling methods that result in representative samples.
Generate a random sample for a statistical question.
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Topic B: Using Sample Data to Draw Inferences About a Population
Analyze data sets using measures of center and interquartile range.
Understand and determine mean absolute deviation (MAD) as a measure of variability of a data set.
Determine the impact of sample size on variability and prediction accuracy.
Estimate population proportions using sample data.
Topic C: Using Sample Data to Compare Two or More Populations
Compare different populations using sample data.
Identify meaningful differences between populations using the mean and mean absolute deviation (MAD) of samples.
The content standards covered in this unit
— Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.
— Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions.
For example, estimate the mean word length in a book by randomly sampling words from the book; predict the winner of a school election based on randomly sampled survey data. Gauge how far off the estimate or prediction might be.
— Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability.
For example, the mean height of players on the basketball team is 10 cm greater than the mean height of players on the soccer team, about twice the variability (mean absolute deviation) on either team; on a dot plot, the separation between the two distributions of heights is noticeable.
— Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations.
For example, decide whether the words in a chapter of a seventh-grade science book are generally longer than the words in a chapter of a fourth-grade science book.
Standards covered in previous units or grades that are important background for the current unit
— Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers.
For example, "How old am I?" is not a statistical question, but "How old are the students in my school?" is a statistical question because one anticipates variability in students' ages.
— Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape.
— Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number.
— Display numerical data in plots on a number line, including dot plots, histograms, and box plots.
— Summarize numerical data sets in relation to their context, such as by:
— Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.
Standards in future grades or units that connect to the content in this unit
— Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets.
— Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).
— 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.
— Understand statistics as a process for making inferences about population parameters based on a random sample from that population.
— Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling.
— Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table. Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible association between the two variables.
For example, collect data from students in your class on whether or not they have a curfew on school nights and whether or not they have assigned chores at home. Is there evidence that those who have a curfew also tend to have chores?
— Make sense of problems and persevere in solving them.
— Reason abstractly and quantitatively.
— Construct viable arguments and critique the reasoning of others.
— Model with mathematics.
— Use appropriate tools strategically.
— Attend to precision.
— Look for and make use of structure.
— Look for and express regularity in repeated reasoning.
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