Learn on PengiIllustrative Mathematics, Grade 7Chapter 8: Probability and Sampling

Lesson 4: Using Samples

In this Grade 7 lesson from Illustrative Mathematics Chapter 8, students use random samples to estimate population measures of center, practicing when to choose mean versus median based on data distribution. They calculate mean absolute deviation (MAD) for real-world data sets — including TV viewer ages and movie ratings — and use MAD to evaluate how variability in a population affects the reliability of a sample estimate. Students apply these skills to draw conclusions and justify answers in context, such as determining whether a film qualifies for an award based on sampled review scores.

Section 1

Comparing Distributions Using Mean and MAD

Property

To compare two distributions, first compare their means to determine which dataset has a higher or lower typical value. Then, compare their Mean Absolute Deviations (MADs) to determine which dataset has more or less variability.

  • A higher mean indicates a greater central value.
  • A larger MAD indicates that the data points are more spread out and less consistent.
  • A smaller MAD indicates that the data points are more clustered around the mean and more consistent.

Section 2

Using percent proportions to make population predictions

Property

A percent proportion can be used to make predictions about a population based on sample data. When we know what percent of a sample has a certain characteristic, we can predict how many individuals in the entire population will have that characteristic.

predicted amount in populationtotal population=percent from sample100\frac{\text{predicted amount in population}}{\text{total population}} = \frac{\text{percent from sample}}{100}

Section 3

Introduction to Variability

Property

Variability is a measure of how much samples or data differ from each other.
Understanding variability in samplings allows students the opportunity to estimate or even measure the differences.
Gauging how far off an estimate or prediction might be is a way to address issues of variation in samples.

Examples

  • One random sample of 10 students reads an average of 3 books a month. A second sample of 10 students reads an average of 4 books. The difference is due to sampling variability.
  • A pollster asks two separate random groups of 100 people if they like a new movie. In the first group, 65% say yes. In the second group, 70% say yes. This 5% difference shows variability.
  • If you roll a die 12 times, you expect to get two 4s. But one time you might get one 4, and the next you might get three. This fluctuation is variability.

Explanation

Variability means that different samples from the same population won't be exactly alike. It's the natural, expected difference between samples. Understanding it helps you know how much you can trust your predictions and how much they might change.

Book overview

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Chapter 8: Probability and Sampling

  1. Lesson 1

    Lesson 1: Probabilities of Single Step Events

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  2. Lesson 2

    Lesson 2: Probabilities of Multi-step Events

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  3. Lesson 3

    Lesson 3: Sampling

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  4. Lesson 4Current

    Lesson 4: Using Samples

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Lesson overview

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Section 1

Comparing Distributions Using Mean and MAD

Property

To compare two distributions, first compare their means to determine which dataset has a higher or lower typical value. Then, compare their Mean Absolute Deviations (MADs) to determine which dataset has more or less variability.

  • A higher mean indicates a greater central value.
  • A larger MAD indicates that the data points are more spread out and less consistent.
  • A smaller MAD indicates that the data points are more clustered around the mean and more consistent.

Section 2

Using percent proportions to make population predictions

Property

A percent proportion can be used to make predictions about a population based on sample data. When we know what percent of a sample has a certain characteristic, we can predict how many individuals in the entire population will have that characteristic.

predicted amount in populationtotal population=percent from sample100\frac{\text{predicted amount in population}}{\text{total population}} = \frac{\text{percent from sample}}{100}

Section 3

Introduction to Variability

Property

Variability is a measure of how much samples or data differ from each other.
Understanding variability in samplings allows students the opportunity to estimate or even measure the differences.
Gauging how far off an estimate or prediction might be is a way to address issues of variation in samples.

Examples

  • One random sample of 10 students reads an average of 3 books a month. A second sample of 10 students reads an average of 4 books. The difference is due to sampling variability.
  • A pollster asks two separate random groups of 100 people if they like a new movie. In the first group, 65% say yes. In the second group, 70% say yes. This 5% difference shows variability.
  • If you roll a die 12 times, you expect to get two 4s. But one time you might get one 4, and the next you might get three. This fluctuation is variability.

Explanation

Variability means that different samples from the same population won't be exactly alike. It's the natural, expected difference between samples. Understanding it helps you know how much you can trust your predictions and how much they might change.

Book overview

Jump across lessons in the current chapter without opening the full course modal.

Continue this chapter

Chapter 8: Probability and Sampling

  1. Lesson 1

    Lesson 1: Probabilities of Single Step Events

    LearnPractice
  2. Lesson 2

    Lesson 2: Probabilities of Multi-step Events

    LearnPractice
  3. Lesson 3

    Lesson 3: Sampling

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  4. Lesson 4Current

    Lesson 4: Using Samples

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