Chapter 3 : Numerical Measures

Chapter 3 : Numerical Measures

1. POPULATION MEAN

   • μ = ( Σ Xi ) / N

2. PARAMETER

   • A measurable characteristic of a population.

3. STATISTIC

   • A measurable characteristic of a sample.

4. SAMPLE MEAN

   • x̄ = ( Σ xi ) / n

5. Arithmetic mean

   • Every set of interval- or ratio-level data has a mean.
   • All the values are included in computing the mean.
   • The mean is unique.
   • The sum of the deviations of each value from the mean is zero.

6. Weighted Mean

   • Σwx/Σw

7. The Median

   • The midpoint of the values after they have been ordered from the smallest to the largest, or the largest to the smallest.

8. The Mode

   • The value of the observation that appears most frequently.

9. The Relative Positions

   • NEGATIVE SKEWNESS
     • mode > median > mean
   • ZERO SKEWNESS
     • mode = median = mean
   • POSITIVE SKEWNESS
     • mode < median < mean

10. The Geometric Mean

11. Mean Deviation

    • The arithmetic mean of the absolute values of the deviations from the arithmetic mean.

12. Variance

    • The arithmetic mean of the squared deviations from the mean.

13. Standard Deviation

    • The square root of the variance