Learn on PengienVision, Mathematics, Grade 7Chapter 6: Use Sampling to Draw Inferences About Populations

Lesson 1: Populations and Samples

In this Grade 7 enVision Mathematics lesson, students learn to distinguish between a population and a sample, and determine whether a sample is representative of a population. The lesson covers key concepts including random sampling, representative samples, and how to generate random samples by assigning numbers to population members. Students also explore how multiple random samples drawn from the same population can vary while still reflecting the broader group.

Section 1

Defining Population and Sample

Property

A population is the entire group of people or objects being studied. A sample is a subset or part of the population that is selected for analysis.

Examples

Section 2

Defining a Representative Sample

Property

A representative sample is a subset of a population whose characteristics accurately reflect the characteristics of the larger population. The proportions of subgroups within the sample (such as age, gender, or other relevant traits) should be similar to their proportions in the overall population.

Examples

  • To find the average allowance of all middle school students in a town, a representative sample would include a proportional number of students from each grade (6th, 7th, and 8th).
  • Surveying only the members of the school basketball team to determine the favorite sport of all students in the school would create a non-representative sample, as it overrepresents students who enjoy basketball.

Explanation

A representative sample is crucial for making accurate generalizations, or inferences, about an entire population. If a sample does not accurately reflect the population, the conclusions drawn from it will be biased and unreliable. The goal of good sampling methods, like random sampling, is to obtain a sample that is as representative as possible.

Section 3

Generating a Simple Random Sample

Property

To generate a simple random sample from a population of size NN for a sample of size nn:

  1. Create a list of all members of the population.
  2. Assign a unique number to each member, from 11 to NN.
  3. Use a random number generator to select nn unique numbers between 11 and NN.
  4. The members of the population corresponding to the generated numbers form the sample.

Examples

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Defining Population and Sample

Property

A population is the entire group of people or objects being studied. A sample is a subset or part of the population that is selected for analysis.

Examples

Section 2

Defining a Representative Sample

Property

A representative sample is a subset of a population whose characteristics accurately reflect the characteristics of the larger population. The proportions of subgroups within the sample (such as age, gender, or other relevant traits) should be similar to their proportions in the overall population.

Examples

  • To find the average allowance of all middle school students in a town, a representative sample would include a proportional number of students from each grade (6th, 7th, and 8th).
  • Surveying only the members of the school basketball team to determine the favorite sport of all students in the school would create a non-representative sample, as it overrepresents students who enjoy basketball.

Explanation

A representative sample is crucial for making accurate generalizations, or inferences, about an entire population. If a sample does not accurately reflect the population, the conclusions drawn from it will be biased and unreliable. The goal of good sampling methods, like random sampling, is to obtain a sample that is as representative as possible.

Section 3

Generating a Simple Random Sample

Property

To generate a simple random sample from a population of size NN for a sample of size nn:

  1. Create a list of all members of the population.
  2. Assign a unique number to each member, from 11 to NN.
  3. Use a random number generator to select nn unique numbers between 11 and NN.
  4. The members of the population corresponding to the generated numbers form the sample.

Examples