Statistics from a grouped frequency distribution

When data are collected into a grouped frequency distribution (a value $x_i$ + its frequency $n_i$), the statistical measures are computed taking the frequencies into account.

Weighted mean: $\bar{x}=\frac{\sum x_i n_i}{N},\quad N=\sum n_i$

Variance and standard deviation: $\sigma^2=\frac{\sum n_i(x_i-\bar{x})^2}{N},\qquad \sigma=\sqrt{\sigma^2}$

The median is the middle value (for which the cumulative frequency reaches $N/2$), and the mode — the value with the largest frequency. The calculator accepts any number of rows — you enter the values and their frequencies.