Class Handout - Particle Size Statistics for Grouped Data, J. M. Cimbala
(Based on data from William C. Hinds, Aerosol Technology, Wiley, New York, 1982.) All diameters in microns, m.
j = class
(bin
number)
D p ,min,j
(lower
limit)
D p ,max, j
(upper
limit)
D p, j
(middle
value)
D p , j =
class
width
1
2
3
4
5
6
7
8
9
10
11
1
4
6
8
9
10
14
16
20
35
50
4
6
8
9
10
14
16
20
35
50
100
2.5
5
7
8.5
9.5
12
15
18
27.5
42.5
75
3
2
2
1
1
4
2
4
15
15
50
J =
n j = n j /D p , j =
f (D p , j ) = probability in this
class =
frequency
count per n j /(D p , j n t )
(count per class width = fraction per f (D p , j )*D p , j =
class)
n j /n t
class width
104
160
161
75
67
186
61
79
90
17
0
34.667
80.000
80.500
75.000
67.000
46.500
30.500
19.750
6.000
1.133
0.000
0.0347
0.0800
0.0805
0.0750
0.0670
0.0465
0.0305
0.0198
0.0060
0.0011
0.0000
11
1000
200
180
160
140
120
nj 100
80
60
40
20
0
0.104
0.264
0.425
0.5
0.567
0.753
0.814
0.893
0.983
1
1
1
90
Plot 1 - Simple
histogram
Plot 2 - Modified
histogram
count per class width
80
70
60
50
40
30
20
10
0
0
10
20
30
40
50
0
10
20
30
Dp
40
50
Dp
0.09
0.09
Plot 3 - Histogram of
fraction per class width
0.08
0.07
0.07
0.06
0.05
0.04
0.03
0.06
0.05
0.04
0.03
0.02
0.02
0.01
0.01
0
0
10
20
30
40
Plot 4 - Probability density
function (PDF), linear
scale
0.08
PDF = f(Dp, j)
f(Dp, j) = fraction per class width
0.104
0.16
0.161
0.075
0.067
0.186
0.061
0.079
0.09
0.017
0
nt =
Totals
0.00
50
0
10
20
Dp
F(Dp, j) = cumulative dist. function
0.08
Plot 5 - PDF,
log scale
0.07
0.06
0.05
0.04
0.03
0.02
0.01
0.00
1
30
40
50
Dp, j
0.09
PDF = f(Dp, j)
F (D p , j ) =
cumulative
distribution
function
10
Dp, j on a log scale
100
1.2
1
0.8
0.6
0.4
Plot 6 - Cumulative
distribution function
0.2
0
0
10
20
30
Dp,max, j
40
50