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)
This assessment accompanies Unit 7 and should be given on the suggested assessment day or after completing the unit.
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distribution
population characteristic
statistical question
population
sample population
sample statistic
sample proportion
representative sample
random sample
measure of center
mean absolute deviation (MAD)
population proportion
mean (average)
range
interquartile range
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7.SP.A.1
Understand and identify populations and sample populations for statistical questions.
7.SP.A.1
Describe sampling methods that result in representative samples.
7.SP.A.1
7.SP.A.2
Generate a random sample for a statistical question.
7.SP.B.3
7.SP.B.4
Analyze data sets using measures of center and interquartile range.
7.SP.B.3
Understand and determine mean absolute deviation (MAD) as a measure of variability of a data set.
7.SP.A.2
Determine the impact of sample size on variability and prediction accuracy.
7.SP.A.2
Estimate population proportions using sample data.
Key: Major Cluster Supporting Cluster Additional Cluster
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