9597

• UCREFRP Catalog Number: 9597
• Author: U.S. Environmental Protection Agency.
• Title: Biological Field and Laboratory Methods for Measuring the Quality of Surface Waters and Effluents.
• USFW Year: 1973.
• USFW - Doc Type: Cincinnati, OH.
• Copyright Material: NO

BIOLOGICAL METHODS

TABLE 3. FREQUENCY TABLE FOR DATA
IN TABLE I GROUPED AT AN INTERVAL
WIDTH OF 20,000 CELLS/ML

Interval

Interval

Frequency

Frequency

0- 20
20 - 40
40 - 60
60 - 80
80 - 100
100 - 120
120 - 140
140 - 160
160 -180
180 - 200

13
11
11
2
1
2
2
2
1
o

200 - 220
220 c 240
240 - 260
260 - 280
280 - 300
300 - 320
320 - 340
340 - 360
360 - 380
380 - 400

o
1
o
o
1
1
o
o
o
o

Closely related to the cumulative frequency
histogram is the cumulative frequency distribu-
tion graph, a graph of relative frequencies. To
obtain the cumulative graph, merely change the
scale of the frequency axis on the cumulative
frequency histogram. The scale change is made
by dividing all values on the scale by the highest
value on the scale (in this case the number of
observations or 48).
The value of the cumulative frequency distri-
bution graph is to allow relative frequency to be
read, i.e., the fraction of observations less than
or equal to some chosen value. Exercise caution
in extrapolating from a cumulative frequency
distribution to other situations. Always bear in
mind that in spite of a planned lack of bias, each
sample, or restricted set of san'F~Cs, is subject to
influences not accounted for and is therefore
unique. This caution is all the more pertinent for
cumulative frequency plots because they tend to

14

10

>-
""
z:
....
=>
e 6
co::
....

40 80 120 160 200 240 280 320
ALGAL CELLS/ML, THOUSANOS

Figure 2. Frequency histogram; interval width is
20,000 cells/mt.

.

smooth out some of the variation noticed in the
frequency histogram. In addition, the phrase
"fraction of observations less than or equal to
some chosen value" can easily be read "fraction
of time the observation is less than or equal to
some chosen value." It is tempting to generalize
from this reading and exten.d tht,se results
beyond their range of applicability.

14

10

>-
""
z:
....
=>
e 6
e:

40 80 120 160 200 240 280 320
ALGAL CELLS/ML, THOUSANDS

Figure 3. Frequency polygon; interval width is
20,000 cells/mt.

50

40

>-
..,
z:
~ 30
~
>
~
~ 20
~

10

o
o 40 80 120 160 200 240 280 320 360 400
ALGAL CEllS/Ml. THOUSANDS

Figure 4. Cumulative frequency histogram; in-
terval width is 10,000 cells/ml.

3.5 Two-dimensional Graphs

Often data are taken where the observations
are recorded as a pair (cell count and time),
(biomass and nutrient concentration). Here a
quick plot of the set of pairs will usually be of
value. Figure 5 is such a graph of data taken
from Table 1. Each point is plotted at a height

.

8