P = mean +/- Z * SD

The average (mean) and the standard deviation (SD) of a human body dimension can be read from the table. There corresponds a specific Z-value with every percentile. Pay attention to the sign + or -. The percentiles above the average have a positive Z-value, the lower percentiles a negative. Some common used examples:

P1 = mean – 2,33 * SD	P99 = mean + 2,33 * SD
P2,5 = mean – 1,96 * SD	P 97,5 = mean + 1,96 * SD
P5 = mean – 1,65 * SD	P 95 = mean + 1,65 * SD
P10 = mean – 1,28 * SD	P90 = mean + 1,28 * SD
P20 = mean – 0,84 * SD	P80 = mean + 0,84 * SD
P25 = mean – 0,67 * SD	P 75 = mean + 0,67 * SD

Example:

The handle of a suitcase that fits 99% of the adult population is:
P99 hand breadth = 83 + 2,33 * 6,9 = 99 mm
An extra of 2 cm gives also some margin for the biggest hand. That makes 12 cm.

To calculate other percentiles, you can look up the corresponding Z-value in this Z-table. In a first step you have to search the desired percentile between all the numbers in the middle. The bold numbers at the outside give the Z-value.

Example:

Percentile 17 hip breadth.
In the Z-table you can find 17,11 which is the closest to 17. The corresponding Z-value is than - 0,95.
P17 = 387 – 0,95 * 35 = 354 mm

Interpreting existing product measures

Z = (X – mean) / SD

Knowing a certain product measure (X), you can calculate the corresponding percentile. Therefore you need the Z-table. At the outside you can read the units and hundredths of the Z-value in bold. Trough combining the row and column, you can find the percentile. Pay attention to the positive or negative sign of the Z-value.

Example:

A man with a body length of 1m92 results in the following Z-value:
Z = (1920 – 1706) / 94 = + 2,28
In the Z-table you can find in the row of 2,2 and the column of 0,08 the percentile 98,87. This means that 98,87% of the population is smaller.

In a kitchen of 90 cm high the lowest point of the wash-up bowl is 75 cm high.
The percentile of the corresponding fist height, determines how many adults will have to bend over.
Z = (750 – 766) / 43 = - 0,37
With this Z-value the percentile 36 of fist height corresponds. This means that everybody who is taller, 64%, will wash-up at a height lower than his fist and will have to bend forward in the back.

Composing men and women or different age classes

mean_A+B= %A . mean_A + %B . mean_B

SD²_A+B = %A . SD²_A+ %B . SD²_B + %A . %B . (mean_A– mean_B)²

To compose two groups, you have to have know their sizes. Above the age of 65 years, there are for example more women (58,65%) than men (41,35%). In the formula this is written as 0,5865 and 0,4135 ! In the adult population men (50,27%) and women (49,73%) are more equally distributed.
When you want to compose different age classes, you have to know that there are considerably more adults (77,7%) than elderly (22,3%). These data of 2004 can be found on the site of the National Institute for Statistics (Belgium).

Example:

The average stature of the Belgian men between 18 and 65 years, is 1766 mm with a standard deviation of 75,4596 mm. For the women these values are 1646 mm and 67,9113 mm respectively. The average body length of the total adult population is:

mean = 0,5027 * 1766 + 0,4973 * 1646 = 1706,32

SD² = 0,5027 * 75,4596² + 0,4973 * 67,9113² + 0,5027 * 0,4973 * (1766 – 1646)²

SD² = 2862,45 + 2293,52 + 3599,90 = 8775,87

SD = 93,6

Adding and subtracting of body dimensions

mean_A_±_B= mean_A ± mean_B

SD²_A_±_B = SD²_A+ SD²_B ± 2 . r . SD_A . SD_B

The correlation coefficient “r” expresses the relation between two body dimensions. A tall person is not per definition fat, so the correlation is low. The table gives estimated correlations between human body dimensions.

	Height	Breadth	Depth
Height	0,65
Breadth	0,30	0,65
Depth	0,20	0,40	0,20

Example:

To determine the height of a computer table, you have to compose the sitting elbow height and the popliteal height. For the adult population this results in the following average and standard deviation:

Mean = 446 + 244 = 690

SD² = 26² + 24² + 2 . 0,65 . 26 . 24 = 2063.2

SD = 45,42

The average height between the floor and the sitting height of the elbows is 690 mm. To calculate the table height an extra of 30 mm for the shoe sole is added. So, the height of a computer table is 72 cm. But to satisfy all the employees, the table should be adjustable:

P1 = mean - 2,33 * SD = 690 - 2,33 * 45,42 = 584 mm + 30 (shoe sole) = 61 cm

P99 = mean + 2,33 * SD = 690 + 2,33 * 45,42 = 789 mm + 30 = 82 cm

An adjustable table between 61 and 82 cm permits 98% of the employees to type at elbow height sitting on a chair with a flat horizontal seating. Office chairs with a tilting mechanism permits the worker to tilt the seating forwards. Therefore the sitting height should be 6 cm above popliteal height. Accordingly the table should be adjustable between 61 and 88 cm.