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Measuring the Central Tendency

  •  Mean (algebraic measure) (sample vs. population):  

\[ {\bar{x}}=\frac{1}{n} \sum_{i=1}^{n}x_{i} \]
\[ \mu = \frac{\sum x}{N} \]

    • Note: n is sample size and N is population size.
    • Weighted arithmetic mean:
    • Trimmed mean: chopping extreme values

\[ {\bar{x}}=\frac{\sum_{i=1}^{n}w_{i}x_{i} }{\sum_{i=1}^{n}w_{i}}  \]

  • Median:
    • Middle value if odd number of values, or average of the middle two values otherwise
    • Estimated by interpolation (for grouped data ):  

\[ median = {L_{1}} + (\frac{\frac{n}{2}-(\sum freq)l)}{freq_{median}}) width \] 


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