Statistics — Formula Sheet

Mean (ungrouped): \bar{x} = \frac{1}{n} \sum_{i=1}^n x_i

Median (n odd): \left(\frac{n+1}{2}\right)^{\text{th}} \text{ observation}

Median (n even): \text{mean of } \left(\frac{n}{2}\right)^{\text{th}} \text{ and } \left(\frac{n}{2}+1\right)^{\text{th}} \text{ observations}

Median (continuous frequency distribution): \text{Median} = l + \frac{\frac{N}{2} - C}{f} \times h

Range of a series = Maximum value – Minimum value

Mean deviation about a value a (ungrouped): \text{M.D.}(a) = \frac{\sum_{i=1}^n |x_i - a|}{n}

Mean deviation about mean (discrete grouped): \text{M.D.}(\bar{x}) = \frac{1}{N} \sum_{i=1}^n f_i |x_i - \bar{x}|

For ungrouped data, M.D.(a) = \frac{\sum_{i=1}^n |x_i - a|}{n}.