Learn on PengiSaxon Math, Course 1Chapter 1: Number, Operations, and Algebra

Investigation 1: Frequency Tables, Histograms, Surveys

In this Grade 6 lesson from Saxon Math, Course 1, students learn how to read and create frequency tables and histograms, including how to organize data into intervals and interpret bar heights. The lesson also introduces surveys, covering key concepts such as population, sample, and closed-option surveys, with real-world examples involving test scores and favorite sports. Students practice representing and analyzing data across all three formats to draw conclusions about larger groups.

Section 1

πŸ“˜ Data Analysis: Frequency Tables & Histograms

New Concept

A frequency table organizes data by counting how often values appear within specific intervals. A histogram is a special bar graph that visually displays this data.

What’s next

This is just the foundation. Next, you'll walk through examples of building and interpreting these tools, and then see how they apply to surveys.

Section 2

Frequency table

Property

A frequency table is a way of pairing selected data, in this case specified test scores, with the number of times the selected data occur.

Examples

  • A class survey shows 5 dogs, 7 cats, and 3 fish. The table would have three rows with frequencies 5, 7, and 3.
  • To track reading progress, you can create bins for pages read: 0-10, 11-20, 21-30, and tally each day's total.
  • A restaurant tracks its most popular dishes by tallying every order for burgers, pizza, and pasta during a lunch rush.

Explanation

Think of a frequency table as a super-organized scorecard for data. Instead of a messy pile of numbers, you create groups (like test score ranges) and use tally marks to track how many fall into each group. It's like being a detective, sorting clues into neat piles to see which pile is biggest! It quickly shows you what's common.

Section 3

Histogram

Property

A histogram is a special type of bar graph. This histogram displays the data (test scores) in equal-size intervals (ranges of scores). There are no spaces between the bars.

Examples

  • A histogram of student heights might have touching bars for intervals like 50βˆ’5450-54 inches, 55βˆ’5955-59 inches, and 60βˆ’6460-64 inches.
  • To show daily temperatures, you can use bars representing ranges like 70βˆ’7570-75 degrees, 76βˆ’8076-80 degrees, and 81βˆ’8581-85 degrees, all connected.
  • Visualizing video game scores can be done with bars showing how many players scored 0βˆ’10000-1000, 1001βˆ’20001001-2000, and 2001βˆ’30002001-3000 points.

Explanation

A histogram is like a city skyline for your data! Each building represents a group of numbers (an interval), and its height shows how many data points are in that group. Unlike regular bar graphs, the buildings in a histogram are always touching, showing that the data flows from one group to the next without any gaps in between.

Section 4

Survey

Property

A survey is a way of collecting data about a population. Rather than collecting data from every member of a population, a survey might focus on only a small part of the population called a sample.

Examples

  • To find the most popular movie in school, you survey 5050 students (the sample) instead of all 500500.
  • A TV network asks 1,0001,000 viewers if they like a new show to decide if it should be renewed for another season.
  • A company gives free cookie samples at a store to predict if the new flavor will be a bestseller nationwide.

Explanation

A survey is like tasting a tiny spoonful of soup to know if the whole pot is delicious. You can't ask everyone in the country their favorite ice cream, so you ask a smaller group (a sample) instead. By studying the sample's answers, you can make a pretty good guess about what the entire population thinks without doing all that work!

Book overview

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

Continue this chapter

Chapter 1: Number, Operations, and Algebra

  1. Lesson 1

    Lesson 1: Adding Whole Numbers and Money

  2. Lesson 2

    Lesson 2: Multiplying Whole Numbers and Money

  3. Lesson 3

    Lesson 3: Unknown Numbers in Addition

  4. Lesson 4

    Lesson 4: Unknown Numbers in Multiplication

  5. Lesson 5

    Lesson 5: Order of Operations, Part 1

  6. Lesson 6

    Lesson 6: Fractional Parts

  7. Lesson 7

    Lesson 7: Lines, Segments, and Rays

  8. Lesson 8

    Lesson 8: Perimeter

  9. Lesson 9

    Lesson 9: The Number Line: Ordering and Comparing

  10. Lesson 10

    Lesson 10: Sequences

  11. Lesson 11Current

    Investigation 1: Frequency Tables, Histograms, Surveys

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

πŸ“˜ Data Analysis: Frequency Tables & Histograms

New Concept

A frequency table organizes data by counting how often values appear within specific intervals. A histogram is a special bar graph that visually displays this data.

What’s next

This is just the foundation. Next, you'll walk through examples of building and interpreting these tools, and then see how they apply to surveys.

Section 2

Frequency table

Property

A frequency table is a way of pairing selected data, in this case specified test scores, with the number of times the selected data occur.

Examples

  • A class survey shows 5 dogs, 7 cats, and 3 fish. The table would have three rows with frequencies 5, 7, and 3.
  • To track reading progress, you can create bins for pages read: 0-10, 11-20, 21-30, and tally each day's total.
  • A restaurant tracks its most popular dishes by tallying every order for burgers, pizza, and pasta during a lunch rush.

Explanation

Think of a frequency table as a super-organized scorecard for data. Instead of a messy pile of numbers, you create groups (like test score ranges) and use tally marks to track how many fall into each group. It's like being a detective, sorting clues into neat piles to see which pile is biggest! It quickly shows you what's common.

Section 3

Histogram

Property

A histogram is a special type of bar graph. This histogram displays the data (test scores) in equal-size intervals (ranges of scores). There are no spaces between the bars.

Examples

  • A histogram of student heights might have touching bars for intervals like 50βˆ’5450-54 inches, 55βˆ’5955-59 inches, and 60βˆ’6460-64 inches.
  • To show daily temperatures, you can use bars representing ranges like 70βˆ’7570-75 degrees, 76βˆ’8076-80 degrees, and 81βˆ’8581-85 degrees, all connected.
  • Visualizing video game scores can be done with bars showing how many players scored 0βˆ’10000-1000, 1001βˆ’20001001-2000, and 2001βˆ’30002001-3000 points.

Explanation

A histogram is like a city skyline for your data! Each building represents a group of numbers (an interval), and its height shows how many data points are in that group. Unlike regular bar graphs, the buildings in a histogram are always touching, showing that the data flows from one group to the next without any gaps in between.

Section 4

Survey

Property

A survey is a way of collecting data about a population. Rather than collecting data from every member of a population, a survey might focus on only a small part of the population called a sample.

Examples

  • To find the most popular movie in school, you survey 5050 students (the sample) instead of all 500500.
  • A TV network asks 1,0001,000 viewers if they like a new show to decide if it should be renewed for another season.
  • A company gives free cookie samples at a store to predict if the new flavor will be a bestseller nationwide.

Explanation

A survey is like tasting a tiny spoonful of soup to know if the whole pot is delicious. You can't ask everyone in the country their favorite ice cream, so you ask a smaller group (a sample) instead. By studying the sample's answers, you can make a pretty good guess about what the entire population thinks without doing all that work!

Book overview

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

Continue this chapter

Chapter 1: Number, Operations, and Algebra

  1. Lesson 1

    Lesson 1: Adding Whole Numbers and Money

  2. Lesson 2

    Lesson 2: Multiplying Whole Numbers and Money

  3. Lesson 3

    Lesson 3: Unknown Numbers in Addition

  4. Lesson 4

    Lesson 4: Unknown Numbers in Multiplication

  5. Lesson 5

    Lesson 5: Order of Operations, Part 1

  6. Lesson 6

    Lesson 6: Fractional Parts

  7. Lesson 7

    Lesson 7: Lines, Segments, and Rays

  8. Lesson 8

    Lesson 8: Perimeter

  9. Lesson 9

    Lesson 9: The Number Line: Ordering and Comparing

  10. Lesson 10

    Lesson 10: Sequences

  11. Lesson 11Current

    Investigation 1: Frequency Tables, Histograms, Surveys