Biological field and laboratory methods for measuring the quality of ...

TABLE 1. RAW DATA ON PLANKTON
COUNTS
Date Count Date Count Date Count
June June July
8 23,077 25 7,692 11 44,231
9 36,538 26 23,077 12 50,000
10 26,923 27 134,615 13 26,923
11 23,077 28 32,692 14 44,231
12 13,462 29 25,000 15 46,154
13 19,231 30 146,154 16 55,768
14 21,154 July 17 9,615
15 61,538 1 107,692 18 13,462
16 96,154 2 13,462 19 3,846
17 23,077 3 9,615 20 3,846
18 46,154 4 148,077 21 11,538
19 48,077 5 53,846 22 7,692
20 51,923 6 103,846 23 13,462
21 50,000 7 78,846 24 21,154
22 292,308 8 132,692 25 17,308
23 165,385 9 228,846
24 42,308 10 307,692
lesser, the larger the value. Closer inspection will
reveal that with the finer interval width (Table
2), the frequency of occurrence does not increase
monotonically as cell count decreases.
Rather, the frequency peak is found in the
interval 20,000 to 30,000 cells/mt. This observation
was not possible using the coarser interval
width; the frequencies were "overintegrated"
and did not reveal this part of the pattern. Finer
interval widths could further change the picture
presented by each of these groupings.
Although a frequency table contains all the
information that a comparable histogram cQntains,
the graphical value of a histogram is
usually worth the small effort required for its
construction. Figures 1 and 2 are frequency
histograms corresponding to Tables 2 and 3,
respectively. It can be seen that the histograms
are more immediately interpretable. The height
of each bar is the frequency of the interval; the
width is the interval width.
3.3 Frequency Polygon
Another way to present essentially the same
informatiqn as that in a frequency histogram is
the use of a frequency polygon. Plot points at
the height of the frequency and at the midpoint
of the interval, and connect the points with
straight lines. The data of Table 3 are used to
7
BIOMETRICS - GRAPHIC EXAMINATION
TABLE 2. FREQUENCY TABLE FOR DATA
IN TABLE 1 GROUPED AT AN INTERVAL
WIDTH OF 10,000 CELLS/ML
Interval
Frequency
Interval
Frequency
O· 10 6 200·210 0
10· 20 7 210·220 0
20· 30 9 220·230 1
30 - 40 2 230·240 0
40· 50 6 240·250 0
50· 60 5 250·260 0
60 - 70 1 260·270 0
70· 80 1 270 - 280 0
80· 90 0 280 - 290 0
90 - 100 1 290·300 1
100 - 110 2 300 - 310 1
110 - 120 0 310 - 320 0
120·130 0 320 - 330 0
130 ·140 2 330·340 0
140·150 2 340 - 350 0
150·160 0 350·360 0
160·170 1 360·370 0
170 - 180 0 370 - 380 0
180 - 190 0 380 - 390 0
190 - 200 0 390·400 0
illustrate the frequency polygon in Figure 3.
3.4 Cumulative Frequency
Cumulative frequency plots are often useful in
data interpretation. As an example, a cumulative
frequency histogram (Figure 4) was constructed
using the frequency table (Table 2 or 3). The
height of a bar (frequency) is the sum of all
frequencies up to and including the one being
plotted. Thus, the first bar will be the same as
the frequency histogram, the second bar equals
the sum of the first and second bars of the
frequency histogram, etc., and the last bar is the
sum of all frequencies.
10
40 120 160 200 240 280 320
ALGAL CELLS/ML, THOUSANOS
Figure 1. Frequency histogram; interval width is
10,000 cells/mt.