TSI Instruments 3936 - Calculation of the Geometric Mean and Geometric Standard Deviation for Number, Surface, and Volume Distributions

C-1
APPENDIX C
Calculation of the
Geometric Mean and
Geometric Standard
Deviation for Number,
Surface, and Volume
Distributions
The information in this appendix can be used with the Aerosol
Instrument Manager
®
for SMPS™ software.
The geometric mean is calculated by equation C-1:
N
dN
d
n
mi
ii
g
∑
=
∆
=
)ln(
ln
Equation C-1
where:
d
g
= geometric mean diameter
d
i
= midpoint diameter for size channel i
N = total concentration
∆
N
i
= concentration within the channel i
m = first channel
n = last channel
The geometric standard deviation (GSD) is calculated by
equation C-2:
1
)ln(ln
ln
2
−
−
=
∑
=
N
ddN
n
mi
gii
g
σ
Equation C-2