Geology Reference
In-Depth Information
from the other. The frequencies or the cumulative frequencies can be expressed
in percentage. Incidentally, in the above example, since the total number of
values is 100, the frequency and its percent are same. If a curve is plotted
taking y-axis as the frequency, it is known as Probability Plot or Probability
Distribution Function (PDF). A number of distribution function based on the
shape of the curve are available. However, among the most common are the
Gaussian/Normal and Log-normal distribution. Some of the estimation tools
work better if the distribution of data values is close to a Gaussian or normal
distribution.
Table 2:
Frequency and cumulative frequency table
Class of
Number of observations/
Cumulative
values
Frequency
Frequency
0-10
1
1
10-20
1
2
20-30
0
2
30-40
0
2
40-50
3
5
50-60
2
7
60-70
2
9
70-80
13
22
80-90
16
38
90-100
11
49
100-110
13
62
110-120
17
79
120-130
13
92
130-140
4
96
140-
4
100
Summary Statistics
The centre of the distribution can be defined by mean, median and mode.
The measure of spread can be defined as variance and standard deviation.
The shape of the distribution is described by the coefficient of skewness and
coefficient of variation. Taken together, these statistics provide feel of the
data.
The mean, m, is the arithmetic average of the data values:
1
n
z
m
=
(1)
i
n
i
1
The number of data is
n
and
z
1
, ....
z
n
are the data values. The mean of the
above presented 100 values is 97.55.
The median,
M
, is the midpoint of the observed values if they are arranged
in increasing order. The median can easily be read from a probability plot.
The mode is the value that occurs most frequently.
