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<br />.
<br />
<br />TABLE 1. RAW DATA ON PLANKTON
<br />COUNTS
<br />
<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 />
<br />.
<br />
<br />lesser, the larger the value. Closer inspection will
<br />reveal that with the finer interval width (Table
<br />2), the frequency of occurrence does not in-
<br />crease monotonically as cell count decreases.
<br />Rather, the frequency peak is found in the
<br />interval 20,000 to 30,000 cells/ml. This observa-
<br />tion was not possible using the coarser interval
<br />width; the frequencies were "overintegrated"
<br />and did not reveal this part of the pattern. Finer
<br />interval widths could further change the picture
<br />presented by each of these groupings.
<br />Although a frequency table contains all the
<br />information that a comparable histogram con-
<br />tains, the graphical value of a histogram is
<br />usually worth the small effort required for its
<br />construction. Figures I and 2 are frequency
<br />histograms corresponding to Tables 2 and 3,
<br />respectively. It can be seen that the histograms
<br />are more immediately interpretable. The height
<br />of each bar is the frequency of the interval; the
<br />width is the interval width.
<br />
<br />3.3 Frequency Polygon
<br />
<br />Another way to present essentially the same
<br />information as that in a frequency histogram is
<br />the use of a frequency polygon. Plot points at
<br />the height of the frequency and at the midpoint
<br />of the interval, and connect the points with
<br />straight lines. The data of Table 3 are used to
<br />
<br />BIOMETRICS - GRAPHIC EXAMINATION
<br />
<br />TABLE 2. FREQUENCY TABLE FOR DATA
<br />IN TABLE I GROUPED AT AN INTERVAL
<br /> WIDTH OF 10,000 CELLS/ML
<br />Interval Frequency Interval Frequency
<br />0- 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 />
<br />illustrate the frequency polygon in Figure 3.
<br />
<br />3.4 Cumulative Frequency
<br />
<br />Cumulative frequency plots are often useful in
<br />data interpretation. As an example, a cumulative
<br />frequency histogram (Figure 4) was constructed
<br />using the frequency table (Table 2 or 3). The
<br />height of a bar (frequency) is the sum of all
<br />frequencies up to and including the one being
<br />plotted. Thus, the first bar will be the same as
<br />the frequency histogram, the second bar equals
<br />the sum of the first and second bars of the
<br />frequency histogram, etc., and the last bar is the
<br />sum of all frequencies.
<br />
<br />10
<br />
<br />
<br />>-
<br />~ 6
<br />....
<br />=
<br />c
<br />....
<br />::::
<br />
<br />40 80 120 160 200 240 280 320
<br />ALGAL CElLSjML. THOUSANDS
<br />
<br />Figure I. Frequency histogram; interval width is
<br />10,000 cells/ml.
<br />
<br />7
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