Study Notes on Stem and Leaf Plots

Introduction to Stem and Leaf Plots

  • Stem and leaf plots are a method of displaying quantitative data in a way that retains the original data values while also providing a visual representation.

Overview of the Exercise

  • The lesson revolves around analyzing a stem and leaf plot that represents the pressure of bicycle tires in pounds per square inch (psi).

Key Components of the Stem and Leaf Plot

  • Title: The title clearly indicates the information being displayed, which is the pressure of bicycle tires.
  • Key: A key explains how to read the data. For example, a stem of '5' and a leaf of '9' together represent a data point of 59 pounds per square inch (psi).

Data Interpretation

  • Stems and Leaves:
    • The left side (stem) indicates the tens place of the pressure values, while the right side (leaf) indicates the units place.
    • Stems and their corresponding Leaves:
    • Stem 5: Leaves 0, 9, 9 → Values: 50, 59, 59
    • Stem 6: Leaf 5 → Value: 65
    • Stem 7: Leaves 2, 4, 6 → Values: 72, 74, 76
    • Stem 8: Leaves 3, 5, 7, 7, 7, 8, 9 → Values: 83, 85, 87, 87, 87, 88, 89
    • Stem 9: Leaves 1, 2, 3, 4, 6, 9 → Values: 91, 92, 93, 94, 96, 99

Questions Presented

  • The instructor presents a question asking which statement is best supported by the data in the stem and leaf plot. The answer choices provided are:
    • A: Half of the tire pressures are 75 pounds per square inch or less.
    • B: There are more tires with pressures from 90 to 99 pounds per square inch than with pressures from 80 to 89 pounds per square inch.
    • C: Three times as many tires have pressures from 50 to 59 pounds per square inch as tires that have a pressure of 65 pounds per square inch.
    • D: There are more tires with pressures from 70 to 79 pounds per square inch than with pressures from 50 to 59 pounds per square inch.

Discussion of Choices

  1. Option A: Check if half the data points (counting) fall at or below 75 psi.
  2. Option B: Count tire pressures from both specified ranges and compare.
  3. Option C: Calculate the number of tires in the two specified ranges (50-59 and 65) to verify the claim of three times as many.
  4. Option D: Compare the counts in the ranges of 70-79 and 50-59 psi to ascertain which is greater.

Student Participation

  • Teacher prompts students to think through the options before selecting a volunteer for an answer.
  • A student named Jacob responded with option C, suggesting it might be the correct choice.

Analyzing Jacob's Response

  • Jacob’s engagement with the question illustrates the method of reasoning students should use.
  • The correctness of his answer requires additional evaluation against actual counts from the stem and leaf plot.