Section 13 Measures of Average

Estimator of central tendency of the data

13.1 Mean

  • Mean or Average or Arithmetic Mean (AM)

\[ \Huge \bar{x} = (x_1 + x_2 + ... + x_n)/n \]

\[ \Huge \bar{x} = \frac{1}{n}\sum\limits_{i=1}^{n} x_{i} \]

  • Mean deviation

  • Centering and Scaling of data

  • Other means: Geometric Mean (GM); Harmonic Mean (HM)

13.2 Median

  • Partition the data into two equal parts
  • 1/2 of observations below & 1/2 of observations above the median

13.3 Mode

  • The most frequent value

13.4 Quartile

  • Partitioning the data into four equal parts
  • Lower quartile: 1/4 of observations are below
  • Upper quartile: 1/4 of observations are above

13.5 Quantile

  • Partitioning the data into n equal parts