Statistics and sampling are important for human performance experiments. Students will learn several sampling types including census, random, stratified random, and convenience. Examples of real-life sampling and experimental design are also shown.

Note: This video is available in both English and Spanish audio, along with corresponding closed captions.

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 MA2015 (2016) Grade: 9-12 Precalculus

45 ) Decide if a specified model is consistent with results from a given data-generating process, e.g., using simulation. [S-IC2]

Example: A model says a spinning coin falls heads up with probability 0.5. Would a result of 5 tails in a row cause you to question the model'

Mathematics MA2015 (2016) Grade: 9-12 Precalculus

46 ) Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each. [S-IC3]

Mathematics MA2015 (2016) Grade: 9-12 Precalculus

48 ) Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant. [S-IC5]

Mathematics MA2015 (2016) Grade: 9-12 Precalculus

49 ) Evaluate reports based on data. [S-IC6]

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.

Mathematics MA2019 (2019) Grade: 7

12. Make informal comparative inferences about two populations using measures of center and variability and/or mean absolute deviation in context.

Unpacked Content

Evidence Of Student Attainment:

Students:

Use measures of center for numerical data from random samples to draw informal comparative inferences about two populations.

Use measures of variability for numerical data from random samples to draw informal comparative inferences about two populations.

Teacher Vocabulary:

Mean

median

mode

Mean absolute deviation

Range

Interquartile range

Knowledge:

Students know:

measures of center are insufficient to compare populations. measures of variability are necessary to assess if data sets are significantly different or not.

Mean is the sum of the numerical values divided by the number of values.

Median is the number that is the midpoint of an ordered set of numerical data.

Mode is the data value or category occurring with the greatest frequency (there can be no mode, one mode, or several modes).

Mean absolute deviation of a data set is found by the following steps: 1) calculate the mean 2) determine the deviation of each variable from the mean 3) divide the sum of the absolute value of each deviation by the number of data points.

Range is a number found by subtracting the minimum value from the maximum. value.

Skills:

Students are able to:

find the measures of center of a data set.

Find the interquartile range of a data set and use to compare variability between data sets.

Understanding:

Students understand that:

outliers skew data, which in turn affects the display.

Measures of center give information about the location of mean, median and mode, whereas measures of variability give information about how spread out the data is.

The mean absolute deviation of a data set describes the average distance that points within a data set are from the mean of the data set.

Diverse Learning Needs:

Essential Skills:

Learning Objectives: M.7.12.1: Define measure of variability, measure of center, inference and mean absolute deviation.
M.7.12.2: Recall how to calculate measure of center and measure of variability.
M.7.12.3: Recall that center is related to measure of center and measure of variability is related to variation.
M.7.12.4: Compare and contrast the measure of center and measure of variability of two numerical data sets.
M.7.12.5: Calculate the mean absolute deviation of a data set in context.

Prior Knowledge Skills:

Describe the center of a set of data in a given distribution.

Compare and contrast the center and variation.

Alabama Alternate Achievement Standards

AAS Standard: M.AAS.7.12 Compare two sets of data within a single data display such as a picture graph, line plot, or bar graph.