Measuring the Central Tendency Mean(algebraic measure)(sample vs. population: x=∑ ∑x Note: n is sample size and / is population size. N a Weighted arithmetic mean Trimmed mean chopping extreme values Middle value if odd number of values, or average of Median: the middle two values otherwise requency 1-5 200 a Estimated by interpolation(for grouped data) 6-15 450 n/2-C∑freq 16-20 300 )width 21-50 1500 Mode fred median 5180 700 a value that occurs most frequently in the data 81-110 44 a Unimodal bimodal, trimodal Empirical formula: mean-mode=3x(mean-median)10 Measuring the Central Tendency ◼ Mean (algebraic measure) (sample vs. population): Note: n is sample size and N is population size. ◼ Weighted arithmetic mean: ◼ Trimmed mean: chopping extreme values ◼ Median: ◼ Middle value if odd number of values, or average of the middle two values otherwise ◼ Estimated by interpolation (for grouped data): ◼ Mode ◼ Value that occurs most frequently in the data ◼ Unimodal, bimodal, trimodal ◼ Empirical formula: = = n i xi n x 1 1   = = = n i i n i i i w w x x 1 1 width freq n freq l median L median ) / 2 ( ) ( 1 = + −  mean − mode = 3(mean − median) N x  =