Learn on PengiReveal Math, AcceleratedUnit 4: Sampling and Statistics

Lesson 4-3: Draw Inferences from Samples

In this Grade 7 lesson from Reveal Math, Accelerated, students learn how to draw inferences about a population by using sample data and proportional reasoning. They practice setting up and solving proportions to estimate percentages and scale sample results to the full population size. The lesson uses real-world contexts like student elections and school club surveys to help students understand how statistics from a random sample can be used to make reasonable predictions.

Section 1

Random Sampling

Property

A random sample is a subset of individuals (a sample) chosen from a larger set (a population). Each individual is chosen randomly and entirely by chance, such that each individual has the same probability of being chosen at any stage during the sampling process, and each subset of kk individuals has the same probability of being chosen for the sample as any other subset of kk individuals. A simple random sample is an unbiased surveying technique.

Examples

  • To find the favorite sport of 500 students, a researcher puts all their names in a bowl and draws 50 names to survey.
  • A quality inspector assigns a number to every one of the 1,000 toys produced and uses a random number generator to select 100 toys to test.
  • To estimate the average number of pages in the library's books, a librarian randomly selects 30 books from the computer catalog to count their pages.

Explanation

Think of this as the fairest way to pick a small group to represent a big one. Everyone has an equal chance of being chosen, like drawing names from a hat. This helps make sure your sample truly reflects the whole population.

Section 2

Making Valid Inferences from Sample Data

Property

An inference is a conclusion about a population based on sample data. Valid inferences can only be made from unbiased samples that are representative, random, and sufficiently large.

Examples

Section 3

Using a Proportion

Property

Set up a proportion where one ratio compares the part to the whole, and the other ratio is the percent rate written in the form of a ratio. Then, solve for the unknown.

partwhole=percent100 \frac{\text{part}}{\text{whole}} = \frac{\text{percent}}{100}

Examples

What number is 120% of 50? Answer: c50=120100→100c=6000→c=60\frac{c}{50} = \frac{120}{100} \rightarrow 100c = 6000 \rightarrow c = 60
20 is what percent of 80? Answer: 2080=x100→80x=2000→x=25\frac{20}{80} = \frac{x}{100} \rightarrow 80x = 2000 \rightarrow x = 25
30 is 60% of what number? Answer: 30x=60100→60x=3000→x=50\frac{30}{x} = \frac{60}{100} \rightarrow 60x = 3000 \rightarrow x = 50

Explanation

Set up a super-fair trade! One fraction is the part over the whole, and the other is the percent over 100. Cross-multiply to find the missing piece. It's like balancing scales to find the unknown value, solving any percent puzzle perfectly.

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Random Sampling

Property

A random sample is a subset of individuals (a sample) chosen from a larger set (a population). Each individual is chosen randomly and entirely by chance, such that each individual has the same probability of being chosen at any stage during the sampling process, and each subset of kk individuals has the same probability of being chosen for the sample as any other subset of kk individuals. A simple random sample is an unbiased surveying technique.

Examples

  • To find the favorite sport of 500 students, a researcher puts all their names in a bowl and draws 50 names to survey.
  • A quality inspector assigns a number to every one of the 1,000 toys produced and uses a random number generator to select 100 toys to test.
  • To estimate the average number of pages in the library's books, a librarian randomly selects 30 books from the computer catalog to count their pages.

Explanation

Think of this as the fairest way to pick a small group to represent a big one. Everyone has an equal chance of being chosen, like drawing names from a hat. This helps make sure your sample truly reflects the whole population.

Section 2

Making Valid Inferences from Sample Data

Property

An inference is a conclusion about a population based on sample data. Valid inferences can only be made from unbiased samples that are representative, random, and sufficiently large.

Examples

Section 3

Using a Proportion

Property

Set up a proportion where one ratio compares the part to the whole, and the other ratio is the percent rate written in the form of a ratio. Then, solve for the unknown.

partwhole=percent100 \frac{\text{part}}{\text{whole}} = \frac{\text{percent}}{100}

Examples

What number is 120% of 50? Answer: c50=120100→100c=6000→c=60\frac{c}{50} = \frac{120}{100} \rightarrow 100c = 6000 \rightarrow c = 60
20 is what percent of 80? Answer: 2080=x100→80x=2000→x=25\frac{20}{80} = \frac{x}{100} \rightarrow 80x = 2000 \rightarrow x = 25
30 is 60% of what number? Answer: 30x=60100→60x=3000→x=50\frac{30}{x} = \frac{60}{100} \rightarrow 60x = 3000 \rightarrow x = 50

Explanation

Set up a super-fair trade! One fraction is the part over the whole, and the other is the percent over 100. Cross-multiply to find the missing piece. It's like balancing scales to find the unknown value, solving any percent puzzle perfectly.