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