Numerical Measures

Numerical Measures

1. central tendency

   • mean = avarage
     • Sum / total numbers
     • Pupulation Mean
       • μ = (Σ * X)/ N
     • sample Mean
       • x̄ = ( Σ xi ) / n
         • x̄ just stands for the “sample mean” Σ means “add up” xi “all of the x-values” n means “the number of items in the sample”
   • median
     • Order the numbers + take the middle number
   • mode = the most frequent observation.
   • weighted mean
     • add and times
       • Image Quality 50%Battery Life 30%Zoom Range 20% The Cony camera gets 8 (out of 10) for Image Quality, 6 for Battery Life and 7 for Zoom Range Cony: 0.5 × 8 + 0.3 × 6 + 0.2 × 7 = 4 + 1.8 + 1.4 = 7.2
   • Rank
     • Percentile = increments of 10%
     • Quartile = increments of 25%

2. Variability

   • the range
     • largest value - smalles value
   • variance
     • The population variance
       • σ2 = Σ ( Xi - μ )2 / N
         • where σ2 is the population variance, μ is the population mean, Xi is the ith element from the population, and N is the number of elements in the population.
     • The sample variance:
       • s2 = Σ ( xi - x )2 / ( n - 1 )
         • where s2 is the sample variance, x is the sample mean, xi is the ith element from the sample, and n is the number of elements in the sample.
   • the standard deviation = the square root of the variance.
     • Population Standard Deviation
       • formula?
     • Sample Standard Deviation
       • formula?