Learn on PengiSaxon Math, Course 2Chapter 4: Lessons 31-40, Investigation 4

Investigation 4: Stem-and-Leaf Plots, Box-and-Whisker Plots

Grade 7 students in Saxon Math Course 2 learn how to organize and analyze data using stem-and-leaf plots and box-and-whisker plots. The lesson covers key statistical measures including mode, range, median, and quartiles, showing students how to identify lower and upper quartiles by dividing a data set into four equal parts. Students then use these five key values — the two extremes, lower quartile, median, and upper quartile — to construct a box-and-whisker plot that displays the distribution of scores along a number line.

Section 1

📘 Stem-and-Leaf Plots, Box-and-Whisker Plots

New Concept

A stem-and-leaf plot organizes data to show its distribution, while a box-and-whisker plot uses a number line to display key values like the median and quartiles.

What’s next

This is your introduction to data visualization. In the following examples, you'll practice creating these plots and calculating the statistical measures they are built on.

Section 2

Stem-and-leaf plot

Property

A stem-and-leaf plot organizes data by separating each value into a 'stem' (the initial digits) and a 'leaf' (the final digit). For example, in the key 3 | 2, the stem 3 and leaf 2 represent the score 3232.

Examples

  • For the scores 14,18,21,21,2514, 18, 21, 21, 25, the plot is:
1 | 4 8
2 | 1 1 5
  • For the scores 52,53,60,68,6952, 53, 60, 68, 69, the plot is:
5 | 2 3
6 | 0 8 9

Explanation

Think of it like organizing your music! The 'stem' is the artist (like 20s, 30s), and the 'leaves' are the individual songs. It’s a super quick way to see the shape of your data without losing any of the original numbers. This clever chart sorts all your values by their first digit, giving a fast, visual summary of the whole group.

Section 3

Median

Property

The median of a set of numbers is the middle number of the set when the numbers are arranged in order. Half of the scores are at or below the median score, and half of the scores are at or above the median score.

Examples

  • In the set of scores 11,14,19,23,2511, 14, 19, 23, 25, the median is 1919.
  • In the set 10,20,30,4010, 20, 30, 40, the median is the average of the two middle numbers: (20+30)÷2=25(20+30) \div 2 = 25.
  • For a set with 35 scores, the median is the 18th value when ordered, since 17 scores will be below it and 17 above.

Explanation

Imagine lining up your classmates by height. The median is the person standing perfectly in the center—not the tallest or shortest, just the middle! If there's an even number of people, the two in the middle find the average height. The median tells you the true midpoint of your data, ignoring any super-tall giants or tiny friends who might skew the average.

Book overview

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Continue this chapter

Chapter 4: Lessons 31-40, Investigation 4

  1. Lesson 1

    Lessons 31: Reading and Writing Decimal Numbers

  2. Lesson 2

    Lessons 32: Metric System

  3. Lesson 3

    Lessons 33: Comparing Decimals, Rounding Decimals

  4. Lesson 4

    Lessons 34: Decimal Numbers on the Number Line

  5. Lesson 5

    Lessons 35: Adding, Subtracting, Multiplying, and Dividing Decimal Numbers

  6. Lesson 6

    Lessons 36: Ratio, Sample Space

  7. Lesson 7

    Lessons 37: Area of a Triangle, Rectangular Area, Part 2

  8. Lesson 8

    Lessons 38: Interpreting Graphs

  9. Lesson 9

    Lessons 39: Proportions

  10. Lesson 10

    Lessons 40: Sum of the Angle Measures of a Triangle, Angle Pairs

  11. Lesson 11Current

    Investigation 4: Stem-and-Leaf Plots, Box-and-Whisker Plots

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

📘 Stem-and-Leaf Plots, Box-and-Whisker Plots

New Concept

A stem-and-leaf plot organizes data to show its distribution, while a box-and-whisker plot uses a number line to display key values like the median and quartiles.

What’s next

This is your introduction to data visualization. In the following examples, you'll practice creating these plots and calculating the statistical measures they are built on.

Section 2

Stem-and-leaf plot

Property

A stem-and-leaf plot organizes data by separating each value into a 'stem' (the initial digits) and a 'leaf' (the final digit). For example, in the key 3 | 2, the stem 3 and leaf 2 represent the score 3232.

Examples

  • For the scores 14,18,21,21,2514, 18, 21, 21, 25, the plot is:
1 | 4 8
2 | 1 1 5
  • For the scores 52,53,60,68,6952, 53, 60, 68, 69, the plot is:
5 | 2 3
6 | 0 8 9

Explanation

Think of it like organizing your music! The 'stem' is the artist (like 20s, 30s), and the 'leaves' are the individual songs. It’s a super quick way to see the shape of your data without losing any of the original numbers. This clever chart sorts all your values by their first digit, giving a fast, visual summary of the whole group.

Section 3

Median

Property

The median of a set of numbers is the middle number of the set when the numbers are arranged in order. Half of the scores are at or below the median score, and half of the scores are at or above the median score.

Examples

  • In the set of scores 11,14,19,23,2511, 14, 19, 23, 25, the median is 1919.
  • In the set 10,20,30,4010, 20, 30, 40, the median is the average of the two middle numbers: (20+30)÷2=25(20+30) \div 2 = 25.
  • For a set with 35 scores, the median is the 18th value when ordered, since 17 scores will be below it and 17 above.

Explanation

Imagine lining up your classmates by height. The median is the person standing perfectly in the center—not the tallest or shortest, just the middle! If there's an even number of people, the two in the middle find the average height. The median tells you the true midpoint of your data, ignoring any super-tall giants or tiny friends who might skew the average.

Book overview

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

Continue this chapter

Chapter 4: Lessons 31-40, Investigation 4

  1. Lesson 1

    Lessons 31: Reading and Writing Decimal Numbers

  2. Lesson 2

    Lessons 32: Metric System

  3. Lesson 3

    Lessons 33: Comparing Decimals, Rounding Decimals

  4. Lesson 4

    Lessons 34: Decimal Numbers on the Number Line

  5. Lesson 5

    Lessons 35: Adding, Subtracting, Multiplying, and Dividing Decimal Numbers

  6. Lesson 6

    Lessons 36: Ratio, Sample Space

  7. Lesson 7

    Lessons 37: Area of a Triangle, Rectangular Area, Part 2

  8. Lesson 8

    Lessons 38: Interpreting Graphs

  9. Lesson 9

    Lessons 39: Proportions

  10. Lesson 10

    Lessons 40: Sum of the Angle Measures of a Triangle, Angle Pairs

  11. Lesson 11Current

    Investigation 4: Stem-and-Leaf Plots, Box-and-Whisker Plots