Learn how the CyberSquad uses sampling and data analysis to help solve a city's trash problem in this interactive from WNET. In the accompanying classroom activity, students watch a series of video clips in which the CyberSquad works to get rid of a mountain of trash by reducing, reusing, and recycling. Students use sampling, multiplication, and fractions to help determine the amount of trash for each method of removal and then complete a sampling and data analysis activity of their own design. This resource is part of the Math at the Core: Middle School Collection.

Content Standard(s):

Mathematics MA2015 (2016) Grade: 7

18 ) 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. [7-SP2]

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.

NAEP Framework

NAEP Statement:: 8DASP1c: Solve problems by estimating and computing with data from a single set or across sets of data.

NAEP Statement:: 8DASP2a: Calculate, use, or interpret mean, median, mode, or range.

NAEP Statement:: 8DASP3a: Given a sample, identify possible sources of bias in sampling.

NAEP Statement:: 8DASP4e: Determine the sample space for a given situation.

Mathematics MA2019 (2019) Grade: 7

10. Examine a sample of a population to generalize information about the population.

a. Differentiate between a sample and a population.

b. Compare sampling techniques to determine whether a sample is random and thus representative of a population, explaining that random sampling tends to produce representative samples and support valid inferences.

c. Determine whether conclusions and generalizations can be made about a population based on a sample.

d. Use data from a random sample to draw inferences about a population with an unknown characteristic of interest, generating multiple samples to gauge variation and making predictions or conclusions about the population.

e. Informally explain situations in which statistical bias may exist.

Unpacked Content

Evidence Of Student Attainment:

Students:

distinguish between a population and a sample population, and identify both for statistical questions.

Understand that a population characteristic is determined using data from the entire population, whereas a sample statistic is determined using data from a sample of the population.

Describe different ways that data can be collected to answer a statistical question.

Understand why a sample of a population may be useful or necessary to answer a statistical question.

Teacher Vocabulary:

Population

Sample

biased

Unbiased

Sampling techniques

Random sampling

Representative samples

Inferences

Knowledge:

Students know:

a random sample can be found by various methods, including simulations or a random number generator.

Samples should be the same size in order to compare the variation in estimates or predictions.

Skills:

Students are able to:

determine whether a sample is random or not and justify their reasoning.

Use the center and variability of data collected from multiple same-size samples to estimate parameters of a population.

Make inferences about a population from random sampling of that population.

Informally assess the difference between two data sets by examining the overlap and separation between the graphical representations of two data sets.

Understanding:

Students understand that:

statistics can be used to gain information about a population by examining a sample of the populations.

Generalizations about a population from a sample are valid only if the sample is representative of that population.

Random sampling tends to produce representative samples and support valid inferences

The way that data is collected, organized and displayed influences interpretation.

Diverse Learning Needs:

Essential Skills:

Learning Objectives: M.7.10.1: Recall how to calculate range, outlier, ratio, and proportion.
M.7.10.2: Define sample, data, variation, prediction, estimation, validity, population, inference, random sampling, statistic, and generalization.
M.7.10.3: Explain the validity of random sampling.
M.7.10.4: Differentiate the appropriate sampling method.
M.7.10.5: Analyze attributes of sample size.
M.7.10.6: Compare and contrast the random sampling data to the population.
M.7.10.7: Compare sample size with population to check for validity.
M.7.10.8: Analyze conclusions of the sample to determine its appropriateness for the population.
M.7.10.9: Predict an outcome of the entire population based on random samplings.
M.7.10.10: Discuss real-world examples of valid sampling and generalizations.
M.7.10.11: Recall the nature of the attribute, how it was measured, and its unit of measure.
M.7.10.12: Collect data from population randomly, choosing same size samples. (Ex. If population is your school, different random samplings should be same number of students).
M.7.10.13: Define and discuss bias.
M.7.10.14: Compare and contrast statistical situations to determine if statistical bias exists.

Prior Knowledge Skills:

Define statistical question.

Calculate the range, mean, median, and mode of a numerical data set.

Recognize the difference between population and sample.

Identify bias from real-world context.

Alabama Alternate Achievement Standards

AAS Standard: M.AAS.7.10 Find the range and median (when given an odd number of data points), and mean (involving one or two-digit numbers) in real-world situations.

Tags:

generalization, population, random sampling, sample, statistics