Basic Algorithms

Since Statistiku has capability to weight the data, we will explain the algorithms in the form of weighted formulas. If you want to apply the formulas for unweighted data, you can set 1s as the weight.

• TOTAL OF FREQUENCY

  `N = \sum_{i=1}^n w_i`

• SUM

  `\text{Sum of} \ X = \sum_{i=1}^n w_i X_i`

• SUM SQUARE

  `\text{Sum square of} \ X = \sum_{i=1}^n w_i X_i^2`

• MEAN

  `\barX = (\sum_{i=1}^n w_i X_i) / N`

• GEOMETRIC MEAN

  `\barX_\text{geom} = \prod_{i=1}^n X_i^(w_i/N)`

• SUM SQUARED TOTAL

  `\text{SST} = \sum_{i=1}^n w_i (X_i - \barX)^2`

• VARIANCE

  Variance of sample:

  `\text{VAR} = \text{SST} / (N-1)`

  Variance of population:

  `\text{VAR}_p = \text{SST} / N`

• STANDARD DEVIATION

  Standard Deviation of sample:

  `\text{SD} = \sqrt{\text{VAR}}`

  Standard Deviation of population:

  `\text{SD}_p = \sqrt{\text{VAR}_p}`

• COVARIANCE

  Covariance of sample:

  `\text{COV} = {\sum_{i=1}^n w_i (X_i - \barX) (Y_i - \barY)} / {N-1}`

  Covariance of population:

  `\text{COV}_p = {\sum_{i=1}^n w_i (X_i - \barX) (Y_i - \barY)} / N`