Learn on PengiSaxon Algebra 1Chapter 7: Rational Expressions and Radicals

Lesson 62: Displaying Data in Stem-and-Leaf Plots and Histograms

In this Grade 9 Saxon Algebra 1 lesson from Chapter 7, students learn how to organize and display numerical data using stem-and-leaf plots and histograms. The lesson covers constructing stem-and-leaf plots with stems, leaves, and keys, then using those plots to calculate statistical measures including median, mode, range, and relative frequency. Students also learn to build histograms that display data frequency across equal intervals, including using a graphing calculator for real-world data sets.

Section 1

๐Ÿ“˜ Displaying Data in Stem-and-Leaf Plots and Histograms

New Concept

A stem-and-leaf plot is a data display that uses some digits as "stems" and others as "leaves."

Whatโ€™s next

Next, youโ€™ll construct and interpret these plots to find key statistical measures and reveal the hidden story within a set of numbers.

Section 2

Stem-and-leaf plot

Property

A data display that uses some digits as "stems" and others as "leaves." The "stems" have a greater place value than the "leaves."

Explanation

Think of it as sorting data by its first digits (the stem) and listing the last digits (the leaves) next to it. This makes it super easy to see how your numbers are spread out, like finding clusters or gaps in test scores! It is a fantastic way to organize data while keeping all the original values visible.

Examples

  • Dataset: 23, 41, 28, 35, 41. Plot: 2|3, 8, 3|5, 4|1, 1. Key: 2|3 = 23.
  • Test scores: 85, 92, 81, 85, 78. Plot: 7|8, 8|1, 5, 5, 9|2. Key: 8|1 = 81.
  • Temperatures: 53, 55, 64, 69. Plot: 5|3, 5, 6|4, 9. Key: 5|3 = 53 degrees.

Section 3

Example Card: Making a Stem-and-Leaf Plot

Let's see how a stem-and-leaf plot can turn a messy list of numbers into a clear picture.

Example Problem

The list shows scores for a recent biology test. Create a stem-and-leaf plot of the data.
88,75,91,84,79,93,68,88,95,75,81,72,90,84,88,6588, 75, 91, 84, 79, 93, 68, 88, 95, 75, 81, 72, 90, 84, 88, 65

Section 4

Example Card: Analyzing a Stem-and-Leaf Plot

Now that our data is organized, let's find its key statistical measures.

Example Problem

Use the plot of ages at a family reunion to find the median, mode, range, and relative frequency of age 71.

Section 5

Histogram

Property

A histogram is a bar graph that displays the frequency of data in equal intervals. Each bar must be the same width and should touch the bar(s) next to it.

Explanation

Imagine sorting data into 'buckets' of the same size, like ages 10-19, 20-29, etc. A histogram uses touching bars to show how many data points fall into each bucket. The taller the bar, the more data is in that group! It provides a great visual summary of the data's distribution without showing every single value.

Examples

  • Data: 5, 8, 11, 12, 19, 21, 23. Intervals: 0-9 (2 items), 10-19 (3 items), 20-29 (2 items).
  • Test Scores: 65, 71, 78, 82, 85, 88, 91, 95. Intervals: 60-69 (1), 70-79 (2), 80-89 (3), 90-99 (2).

Book overview

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

Continue this chapter

Chapter 7: Rational Expressions and Radicals

  1. Lesson 1

    Lesson 61: Simplifying Radical Expressions

  2. Lesson 2Current

    Lesson 62: Displaying Data in Stem-and-Leaf Plots and Histograms

  3. Lesson 3

    Lesson 63: Solving Systems of Linear Equations by Elimination

  4. Lesson 4

    Lesson 64: Identifying, Writing, and Graphing Inverse Variation

  5. Lesson 5

    Lesson 65: Writing Equations of Parallel and Perpendicular Lines

  6. Lesson 6

    Lesson 66: Solving Inequalities by Adding or Subtracting

  7. Lesson 7

    Lesson 67: Solving and Classifying Special Systems of Linear Equations

  8. Lesson 8

    Lesson 68: Mutually Exclusive and Inclusive Events

  9. Lesson 9

    Lesson 69: Adding and Subtracting Radical Expressions

  10. Lesson 10

    Lesson 70: Solving Inequalities by Multiplying or Dividing

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

๐Ÿ“˜ Displaying Data in Stem-and-Leaf Plots and Histograms

New Concept

A stem-and-leaf plot is a data display that uses some digits as "stems" and others as "leaves."

Whatโ€™s next

Next, youโ€™ll construct and interpret these plots to find key statistical measures and reveal the hidden story within a set of numbers.

Section 2

Stem-and-leaf plot

Property

A data display that uses some digits as "stems" and others as "leaves." The "stems" have a greater place value than the "leaves."

Explanation

Think of it as sorting data by its first digits (the stem) and listing the last digits (the leaves) next to it. This makes it super easy to see how your numbers are spread out, like finding clusters or gaps in test scores! It is a fantastic way to organize data while keeping all the original values visible.

Examples

  • Dataset: 23, 41, 28, 35, 41. Plot: 2|3, 8, 3|5, 4|1, 1. Key: 2|3 = 23.
  • Test scores: 85, 92, 81, 85, 78. Plot: 7|8, 8|1, 5, 5, 9|2. Key: 8|1 = 81.
  • Temperatures: 53, 55, 64, 69. Plot: 5|3, 5, 6|4, 9. Key: 5|3 = 53 degrees.

Section 3

Example Card: Making a Stem-and-Leaf Plot

Let's see how a stem-and-leaf plot can turn a messy list of numbers into a clear picture.

Example Problem

The list shows scores for a recent biology test. Create a stem-and-leaf plot of the data.
88,75,91,84,79,93,68,88,95,75,81,72,90,84,88,6588, 75, 91, 84, 79, 93, 68, 88, 95, 75, 81, 72, 90, 84, 88, 65

Section 4

Example Card: Analyzing a Stem-and-Leaf Plot

Now that our data is organized, let's find its key statistical measures.

Example Problem

Use the plot of ages at a family reunion to find the median, mode, range, and relative frequency of age 71.

Section 5

Histogram

Property

A histogram is a bar graph that displays the frequency of data in equal intervals. Each bar must be the same width and should touch the bar(s) next to it.

Explanation

Imagine sorting data into 'buckets' of the same size, like ages 10-19, 20-29, etc. A histogram uses touching bars to show how many data points fall into each bucket. The taller the bar, the more data is in that group! It provides a great visual summary of the data's distribution without showing every single value.

Examples

  • Data: 5, 8, 11, 12, 19, 21, 23. Intervals: 0-9 (2 items), 10-19 (3 items), 20-29 (2 items).
  • Test Scores: 65, 71, 78, 82, 85, 88, 91, 95. Intervals: 60-69 (1), 70-79 (2), 80-89 (3), 90-99 (2).

Book overview

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

Continue this chapter

Chapter 7: Rational Expressions and Radicals

  1. Lesson 1

    Lesson 61: Simplifying Radical Expressions

  2. Lesson 2Current

    Lesson 62: Displaying Data in Stem-and-Leaf Plots and Histograms

  3. Lesson 3

    Lesson 63: Solving Systems of Linear Equations by Elimination

  4. Lesson 4

    Lesson 64: Identifying, Writing, and Graphing Inverse Variation

  5. Lesson 5

    Lesson 65: Writing Equations of Parallel and Perpendicular Lines

  6. Lesson 6

    Lesson 66: Solving Inequalities by Adding or Subtracting

  7. Lesson 7

    Lesson 67: Solving and Classifying Special Systems of Linear Equations

  8. Lesson 8

    Lesson 68: Mutually Exclusive and Inclusive Events

  9. Lesson 9

    Lesson 69: Adding and Subtracting Radical Expressions

  10. Lesson 10

    Lesson 70: Solving Inequalities by Multiplying or Dividing