Section 2

Section 2.1: Data Types and Levels of Measure

Types of Variables

  • Quantitative Variables: Numerical measures of individuals, categorized into:

    • Interval: Differences in values have meaning but no true zero.

    • Ratio: Has properties of interval variables, with meaningful ratios and a true zero.

  • Qualitative Variables: Categorical classifications, further divided into:

    • Nominal: Names, labels, and categories with no specific order.

    • Ordinal: Can be ranked or arranged in a specific order.

Examples of Variable Types

  • Categorical Variables:

    • A. Amount spent on CDs: Quantitative

    • B. Television screen type: Qualitative

    • C. TV brands: Qualitative

    • D. Ages in the room: Quantitative

    • E. Crayon colors: Qualitative

    • F. Number of stories in a building: Quantitative

Section 2.2: Dealing With Errors

Types of Measurement Errors

  • Random Errors: Vary with each measurement.

  • Systematic Errors: Constant errors affecting measurements in the same way each time.

Examples

  • Systematic Error: Digital scale shows -1.3 pounds when unloaded (affects all measurements similarly).

  • Random Error: Regular scale bounces around and gives inconsistent readings.

Measuring Error Significance

  • Absolute Error: Distance from the true value. Formula: Absolute error = Measured value – True value

  • Relative Error: Absolute error in comparison to the true value. Formula: Relative error = (Absolute error / True value) x 100%

Accuracy vs. Precision

  • Accuracy: Closeness to the true value.

  • Precision: Level of detail in a measurement.

Section 2.3: Uses of Percentages in Statistics

Converting Percentages, Fractions, and Decimals

  • Conversion methods discussed for percentage, decimal, and fraction.

Changes Described in Percentages

  • Absolute Change: Actual increase or decrease. Formula: Absolute change = New value – Reference value

  • Relative Change: Size of absolute change as a fraction of the reference value.

Example of Salary Increase Comparison

  • Absolute increase:

    • Clint: 28000 - 20000 = 8000 (Clint's salary increase).

    • Helen: 35000 - 25000 = 10000 (Helen's salary increase).

  • Relative increase results show both are equal in terms of percentage change.

Section 2.4: Index Numbers

Definition and Calculation

  • Index Number: Compares measurements over time or locations.

  • Formula for the index number: (Value / Reference Value) x 100.

Example Calculation

  • Gasoline prices in 2012 vs. 1960.

    • 2012 Price: $3.44, Reference: $0.31.

    • Index number: (344 / 31) x 100 = 1110.

Comparing Index Numbers

  • Example comparing gasoline prices in 2010 and 1970 shows significant increase.

Consumer Price Index (CPI)

  • Measures actual prices against inflation rates.

  • Example calculating CPI effect on toy price over years to adjust for inflation.

Rate of Inflation Calculation

  • Relative change in CPI gives inflation rate between years. Formula: (CPI Year 2 - CPI Year 1) / CPI Year 1.

  • Example calculates salary adjustment for inflation over years.