Formulas
Calculating
percentiles
Interpreting
existing product measures
Composing
men and women or age classes
Adding
and subtracting of body dimensions
Calculating
percentiles
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 Zvalue with every percentile. Pay attention to
the sign + or . The percentiles above the average have a
positive Zvalue, 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
Zvalue in this Ztable.
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 Zvalue.
Example:
Percentile
17 hip breadth.
In the Ztable you can find 17,11 which is the closest to
17. The corresponding Zvalue 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 Ztable.
At the outside you can read the units and hundredths of the
Zvalue in bold. Trough combining the row and column, you
can find the percentile. Pay attention to the positive or
negative sign of the Zvalue.
Example:
A
man with a body length of 1m92 results in the following Zvalue:
Z = (1920 – 1706) / 94 = + 2,28
In the Ztable 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 washup 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 Zvalue the percentile 36 of fist height corresponds.
This means that everybody who is taller, 64%, will washup
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.