Statistics

Calculates the arithmetic mean of a set of n observations.

Gives the midpoint value that represents a continuous class interval.

Computes the arithmetic mean for grouped or frequency distribution data.

Calculates the mean using deviations from an assumed mean a to simplify arithmetic.

Calculates the mean for equal class width h using scaled deviation step values.

Gives the pooled arithmetic mean of two groups having sizes n₁ and n₂.

Finds the middle observation of an arranged numerical dataset.

Computes the median from the median class of a continuous frequency distribution.

Calculates the mode for continuous grouped data from the modal class.

Approximates the relationship between the three central tendencies for moderately skewed distributions.

Measures statistical dispersion as the difference between extreme values.

Calculates the mean absolute deviation of observations from their arithmetic mean.

Calculates the mean absolute deviation of observations taken about their median.

Computes the variance of n individual observations from raw sums of squares and mean.

Defines standard deviation as the positive square root of the variance.

Calculates the variance of a frequency distribution using frequencies and class marks.

Gives the exact variance for the first n consecutive natural numbers 1, 2, ..., n.

Shows that a change of origin by b and scale by a shifts the mean accordingly.

Shows that variance is independent of change of origin and scales quadratically.

Calculates the combined variance of two pooled datasets with different sizes and means.

Measures relative variability to compare consistency across distributions with positive means.

States that the sum of squared deviations is strictly minimised when taken about the mean.