Understanding Fractions, Percents, and Data Analysis

Sep 1, 2024

Lecture Notes: Co-requisite Support Activity 1E

Overview

  • Focus on fractions, decimals, and now, percents.
  • Introduction to contingency tables (two-way tables) for future familiarity.

Fractions, Decimals, and Percents

  • Fractions, Decimals, Percents: Different ways to describe a proportion.
    • Example: 3/4 as a fraction, 0.75 as a decimal, 75% as a percent.
  • Conversion:
    • Fraction to Decimal: Divide top by bottom (e.g., 3/4 = 0.75).
    • Decimal to Percent: Move decimal two places to the right.
  • Adding Zeros: Can add zeros after a decimal without changing its value (e.g., 0.6 = 0.60).

Rounding Decimals

  • Understanding Place Values:
    • Tenths, hundredths, thousandths, ten-thousandths.
    • Round to a specific place value based on the digit to the right.
  • Rounding Rule: If the digit to the right is 5 or greater, round up.
  • Tip: Think about decimals in terms of money to simplify rounding.

Contingency Tables (Two-Way Tables)

  • Structure:
    • Rows and columns represent different groups and attributes.
    • Subtotals at the edges, grand total at the intersection.
  • Purpose: Breakdown of data by two different characteristics.
    • Example: Students' living status (on/off campus) and library preference.

Examples and Exercises

Example 1: Fractions to Decimals and Rounding

  • Convert 5/8 to a decimal: 0.625
  • Rounding:
    • Nearest tenth: 0.6
    • Nearest hundredth: 0.63
    • Nearest thousandth: 0.625

Example 2: Using a Contingency Table

  • Context: Students in a statistics class, divided by living status and library preference.
  • Data Interpretation:
    • Total students: 150
    • On campus: 45, Off campus: 105
    • Library preference: 20 on campus, 40 off campus prefer library.
  • Fill in Table: Use given data and simple subtraction to complete table.

Proportion Calculations

  • Calculate proportions using part over whole method.
  • Convert results to fraction, decimal, and percent.
  • Example questions:
    • Proportion of students living on campus and preferring the library.

Important Concepts

  • Proportion: Part divided by whole.
  • Percent Conversion: Multiply result by 100 and add percent symbol.
  • Analysis: Use completed table for comparison and analysis.

Conclusion

  • Understanding contingency tables and proportions will aid in analyzing data later in the semester.
  • Practice with these concepts will make future complex topics more approachable.
  • Remember, the key is not just calculating but also interpreting the data meaningfully.

Next Steps: Continue to practice these concepts and be ready to apply them in upcoming assessments.