Learn on PengiReveal Math, AcceleratedUnit 4: Sampling and Statistics

Lesson 4-1: Relationships between Populations, Samples, and Statistics

In this Grade 7 lesson from Reveal Math, Accelerated, students learn to distinguish between populations and samples, and between parameters and statistics, understanding that a parameter is calculated from every member of a population while a statistic is calculated from a sample to estimate that parameter. Using real-world contexts like tongue-rolling studies and voter surveys, students practice identifying which type of value a given percentage represents and explaining their reasoning. This lesson builds foundational vocabulary and concepts for Unit 4's broader study of sampling and statistics.

Section 1

Defining Population and Sample

Property

A population is the complete set of all individuals or items that we want to study and draw conclusions about. A sample is a subset of the population that is actually observed or measured to gather data.

Examples

Section 2

Distinguishing Between Parameters and Statistics

Property

  • Parameter: A numerical value that describes a characteristic of an entire population.
  • Statistic: A numerical value that describes a characteristic of a sample.

A helpful mnemonic to remember the relationship is:

  • Population →\rightarrow Parameter
  • Sample →\rightarrow Statistic

Section 3

Computing a Sample Percent

Property

A sample percent is a statistic that describes the proportion of a sample that shares a specific characteristic. To compute a sample percent, divide the number of items in the sample with the characteristic by the total sample size, then multiply by 100100.

Sample Percent=Part of SampleTotal Sample Size×100\text{Sample Percent} = \frac{\text{Part of Sample}}{\text{Total Sample Size}} \times 100

Section 4

Computing a Sample Mean

Property

A sample mean is a statistic that represents the average of a subset of data drawn from a larger population. It is calculated by adding all the data values in the sample and dividing by the total number of values in that sample.

Sample Mean=Sum of sample valuesNumber of values in the sample\text{Sample Mean} = \frac{\text{Sum of sample values}}{\text{Number of values in the sample}}

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Defining Population and Sample

Property

A population is the complete set of all individuals or items that we want to study and draw conclusions about. A sample is a subset of the population that is actually observed or measured to gather data.

Examples

Section 2

Distinguishing Between Parameters and Statistics

Property

  • Parameter: A numerical value that describes a characteristic of an entire population.
  • Statistic: A numerical value that describes a characteristic of a sample.

A helpful mnemonic to remember the relationship is:

  • Population →\rightarrow Parameter
  • Sample →\rightarrow Statistic

Section 3

Computing a Sample Percent

Property

A sample percent is a statistic that describes the proportion of a sample that shares a specific characteristic. To compute a sample percent, divide the number of items in the sample with the characteristic by the total sample size, then multiply by 100100.

Sample Percent=Part of SampleTotal Sample Size×100\text{Sample Percent} = \frac{\text{Part of Sample}}{\text{Total Sample Size}} \times 100

Section 4

Computing a Sample Mean

Property

A sample mean is a statistic that represents the average of a subset of data drawn from a larger population. It is calculated by adding all the data values in the sample and dividing by the total number of values in that sample.

Sample Mean=Sum of sample valuesNumber of values in the sample\text{Sample Mean} = \frac{\text{Sum of sample values}}{\text{Number of values in the sample}}