Mean, mode, median and deviation

The mean is x̄ = (x₁ + … + xₙ)/n; for a frequency table x̄ = (n₁x₁ + … + nₖxₖ)/n. The mode is the most frequent variant (there may be several modes). The median is the middle value of the variation series: the (n + 1)/2-th term if n is odd, and the average of the n/2-th and (n/2 + 1)-th terms if n is even. A single large value changes the mean noticeably but hardly affects the median. The range is the difference between the largest and smallest variants. The standard deviation shows how widely the data are spread around the mean: sₙ = √(Σ(xᵢ − x̄)²/n), and for a frequency table √(Σnᵢ(xᵢ − x̄)²/Σnᵢ). If all values are equal, sₙ = 0; the greater the spread, the greater sₙ. For data grouped into intervals the mean is found approximately using the midpoint of each interval.