Classroom Resource

Human Performance & Sampling

Subject Area

Mathematics

Grade(s)

7, 9, 10, 11, 12

Overview

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.

Mathematics (2019) Grade(s): 7

MA19.7.10

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

Unpacked Content

UP:MA19.7.10

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.
Mathematics (2019) Grade(s): 7

MA19.7.12

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

Unpacked Content

UP:MA19.7.12

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.
Mathematics (2019) Grade(s): 7 - Grade 7 Accelerated

MA19.7A.26

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

Unpacked Content

UP:MA19.7A.26

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.
Mathematics (2019) Grade(s): 7 - Grade 7 Accelerated

MA19.7A.28

Make informal comparative inferences about two populations using measures of center and variability and/or mean absolute deviation in context. [Grade 7, 12]

Unpacked Content

UP:MA19.7A.28

Vocabulary

  • Mean
  • Median
  • Mode
  • Mean absolute deviation

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.
Mathematics (2019) Grade(s): 09-12 - Algebra II with Statistics

MA19.A2.26

Describe the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each.

Unpacked Content

UP:MA19.A2.26

Vocabulary

  • Sample surveys
  • Experiments
  • Observational studies
  • Randomization

Knowledge

Students know:
  • Key components of sample surveys, experiments, and observational studies.
  • Procedures for selecting random samples.

Skills

Students are able to:
  • Use key characteristics of sample surveys, experiments, and observational studies to select the appropriate technique for a particular statistical investigation.

Understanding

Students understand that:
  • Sample surveys, experiments, and observational studies may be used to make inferences made about the population.
  • Randomization is used to reduce bias in statistical procedures.
Mathematics (2019) Grade(s): 09-12 - Algebra II with Statistics

MA19.A2.33

Use data from a randomized experiment to compare two treatments; limit to informal use of simulations to decide if an observed difference in the responses of the two treatment groups is unlikely to have occurred due to randomization alone, thus implying that the difference between the treatment groups is meaningful.

Unpacked Content

UP:MA19.A2.33

Vocabulary

  • Randomized experiment
  • Significant
  • Parameters

Knowledge

Students know:
  • Techniques for conducting randomized experiments.
  • Techniques for conducting simulations of randomized experiment situations.

Skills

Students are able to:
  • Design and conduct randomized experiments with two treatments.
  • Draw conclusions from comparisons of the data of the randomized experiment.
  • Design, conduct, and use the results from simulations of a randomized experiment situation to evaluate the significance of the identified differences.

Understanding

Students understand that:
  • Differences of two treatments can be justified by a significant difference of parameters from a randomized experiment.
  • Statistical analysis and data displays often reveal patterns in data or populations, enabling predictions.
Link to Resource
https://aptv.pbslearningmedia.org/resource/f657a984-9b44-4e15-a06e-27dc856fe810…

CR Resource Type

Audio/Video

Resource Provider

PBS
Accessibility

Accessibility

Video resources: includes closed captioning or subtitles
License

License Type

Custom

Custom License Type (URL)

https://aptv.pbslearningmedia.org/help/terms-of-use/#.YD-bCNhKiUk

Comments or Notes

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

Approved Date

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