# How it works - 1D Formulas

### Basic calculations with data

The body variables are divided according to the Dutch standard eel partitioning. This means that using the average (P50) and the standard deviation an estimation can be found for other percentiles. The following formula can be used for this:

x_p = \bar{x} + z_p \cdot s

The Z-value can be found in a table which consists of overshooting chances for the eel partitioning. (look at het z-value table). The remaining population after dimensioning can be found by turning the formula.

z_p = \frac{x_p - \bar{x}}{s}

Now the overshooting percentage can be found in the z-value table.

### Determining mixed population

To get to a mixed population (g) consisting of a group of men (m) and a group of women (v), the next fomula's can be used:

\bar{x}_g = \frac{n_m}{n_m + n_v} \cdot \bar{x}_m + \frac{n_v}{n_m + n_v} \cdot \bar{x}_v

{s_g}^2 = \frac{n_m}{n_m + n_v} \cdot {s_m}^2 + \frac{n_v}{n_m + n_v} \cdot {s_v}^2 + \frac{n_m \cdot n_v}{(n_m + n_v)^2} \cdot (\bar{x}_1 - \bar{x}_2 )^2

When both groups are equal size, this results in the followinf formula:

\bar{x}_g = \frac{1}{2} \cdot (\bar{x}_m + \bar{x}_v)

{s_g}^2 = \frac{1}{2} \cdot {s_m}^2 + \frac{1}{2} \cdot {s_v}^2 + \frac{1}{4} \cdot (\bar{x}_m - \bar{x}_v)^2

### Determining the distribution of 2 added measures

To add or substract two measures, the next formulas can be used (only when the measures are in length of each other)

\bar{x}_3 = \bar{x}_1 + \bar{x}_2

{s_3}^2 = {s_1}^2 + {s_2}^2 \pm 2 \cdot r \cdot s_1 \cdot s_2

For the combining of measures a table with estimations of correlations can be used.

### Determining remaining population

For calculating the remaining suited population (Pz) after dimentioning of a subject in two dimensions, for which (Px) respectivly (Py) are the percentages, the next formula applies (only if Px is smaller or equals Py)

P_z = P_x \cdot P_y + r^2 \cdot (P_x - Px \cdot P_y)