# Basic Statistics¶

Basic statistics algorithm computes the following set of quantitative dataset characteristics:

• minimums/maximums

• sums

• means

• sums of squares

• sums of squared differences from the means

• second order raw moments

• variances

• standard deviations

• variations

 Operation Computational methods Programming Interface dense dense compute(…) compute_input compute_result

## Mathematical formulation¶

### Computing¶

Given a set $$X$$ of $$n$$ $$p$$-dimensional feature vectors $$x_1 = (x_{11}, \ldots, x_{1p}), \ldots, x_n = (x_{n1}, \ldots, x_{np})$$, the problem is to compute the following sample characteristics for each feature in the data set:

Statistic

Definition

Minimum

$$min(j) = \smash{\displaystyle \min_i } \{x_{ij}\}$$

Maximum

$$max(j) = \smash{\displaystyle \max_i } \{x_{ij}\}$$

Sum

$$s(j) = \sum_i x_{ij}$$

Sum of squares

$$s_2(j) = \sum_i x_{ij}^2$$

Means

$$m(j) = \frac {s(j)} {n}$$

Second order raw moment

$$a_2(j) = \frac {s_2(j)} {n}$$

Sum of squared difference from the means

$$\text{SDM}(j) = \sum_i (x_{ij} - m(j))^2$$

Variance

$$k_2(j) = \frac {\text{SDM}(j) } {n - 1}$$

Standard deviation

$$\text{stdev}(j) = \sqrt {k_2(j)}$$

Variation coefficient

$$V(j) = \frac {\text{stdev}(j)} {m(j)}$$

### Computation method: dense¶

The method computes the basic statistics for each feature in the data set.

## Programming Interface¶

Refer to API Reference: Basic statistics.