📊 Statistics

1. Measures of Dispersion

Dispersion is the measure of the variation of the items. Common measures include Range, Quartile Deviation, Mean Deviation, and Standard Deviation.

The arithmetic mean of the absolute deviations of the values from an average (mean or median).

M.D. = (1/N) Σ |x_i - a| Where 'a' is the central tendency (mean or median) and N is total frequency.

Variance (σ²): The mean of the squares of the deviations from the mean.

Standard Deviation (σ): The positive square root of the variance. It is the most widely used measure of dispersion.

σ = √ [ (1/N) Σ f_i (x_i - x̄)² ] Standard Deviation Formula for grouped data. x̄ is the mean.

To compare the variability of two series with different units or different means, we use C.V.

C.V. = (σ / x̄) × 100

The series having greater C.V. is said to be more variable. The series having lesser C.V. is said to be more consistent (or stable).