Frequency cumulative

Order number,y FaUure times, /, km Cumulative frequency,, %... 

Cumulative frequency data, whethei on a number, surface area, or mass basis, allows for easy estimates of the total number, surface area, or mass of particles less than a given size. For the data in Table 1, 12 particles out of 1000 (1.2%) had a diameter less than 2 p.m, 7.4% less than 4 p.m, etc. 

Fig. 3. Cumulative frequency distribution plotted by A, number B, surface area and C, volume, for the data in Table 1.

A frequency distribution cui ve can be used to plot a cumulative-frequency cui ve. This is the cui ve of most importance in business decisions and can be plotted from a normal frequency distribution cui ve (see Sec. 3). The cumulative cui ve represents the probability of a random value z having a value of, say, Z or less. 

If necessary, the fit can be improved by increasing the order of the polynomial part of Eq. (9-89), so that this approach provides a veiy flexible method of simulation of a cumulative-frequency distribution. The method can even be extended to J-shaped cui ves, which are characterized by a maximum frequency at x = 0 and decreasing frequency for increasing values of x, by considering the reflexion of the cui ve in the y axis to exist. The resulting single maximum cui ve can then be sampled correctly by Monte Carlo methods if the vertical scale is halved and only absolute values of x are considered. 

The cumulative-frequency function calculated from this simple expression is compared with the precise value in Table 9-10. 

When a cumulative-frequency curve can be satisfactorily represented by a logistics cuiwe, the underlying frequency cui ve can be obtained by differentiation of Eq. (9-91) as... 

Figures 12 and 13 illustrate two of the more commonly used methods for displaying societal risk results (1) an F-N curve and (2) a risk profile. The F-N curve plots the cumulative frequencies of events causing N or more impacts, with the number of impacts (N) shown on the horizontal axis. With the F-N curve you can easily see the expected frequency of accidents that could harm greater than a specified number of people. F-N curve plots are almost always presented on logarithmic scales because of...

A graphical illustration of the cumulative frequency (F) of accidents resulting in a consequence of greater than or equal to N impacts. A way of illustrating societal risk... 

Figure 4.4 Cumulative frequency and histogram for grouped data set...

Figure 4.5 Cumulative frequency plot and determination of mean and standard deviation graphically...

Figure 4.10 Cumulative frequency distribution for SAE 1018 yield strength data...

Mid-class (newtons) F requency (%) Frequency (xlO) W= 1000 Cumulative frequency (0 z-0.3 lii(mid-class) (x-axis) lnln(l/(l -F, (j-axis)... 

Larsen (18-21) has developed averaging time models for use in analysis and interpretation of air quality data. For urban areas where concentrations for a given averaging time tend to be lognormally distributed, that is, where a plot of the log of concentration versus the cumulative frequency of occurrence on a normal frequency distribution scale is nearly linear,... 

The use of various statistical techniques has been discussed (46) for two situations. For standard air quality networks with an extensive period of record, analysis of residuals, visual inspection of scatter diagrams, and comparison of cumulative frequency distributions are quite useful techniques for assessing model performance. For tracer studies the spatial coverage is better, so that identification of meiximum measured concentrations during each test is more feasible. However, temporal coverage is more limited with a specific number of tests not continuous in time. 

F-N curve - A cumulative frequency number affected curve. 

Figure 7 provides a cumulative frequency distribution of the maximum 8-hour standard In 15 cities In 1980-84. Shown on the graph Is the 10 mg/m3 WHO guideline value. It can be seen that the average maximum 8-hour level Is exceeded In about 50% of the cities. 

Since one is only rarely interested in the density at a precise point on the z-axis, the cumulative probability (cumulative frequency) tables are more important in effect, the integral from -oo to +z over the probability density function for various z > 0 is tabulated again a few entries are given in Fig. 1.13. 

Assignments X ) (length = N) U() (length = NB) VO (length = MB) W() (length =NB) XMIN XMAX IL IH W values to be analyzed number of observations per bin frequency of observation (%) per bin cumulative frequencies smallest x-value largest x-value number of observations x smaller x in number of observations x larger x ax width of a bin... 

Cumulative Frequency Distribution of 3 D-optimal sampling times... 

Figure 3.7 Frequency and cumulative frequency distributions of 3D-optimal sampling times for the Gompertz model, given the observations for subject 4. Vertical lines split the cumulative empirical distribution into equal probability regions.

Method III is called a "Histogram Plot" while Methods I n are called "Frequency Plot" and "Cumulative Frequency Plot", respectively. There is one important point which needs to be emphasized. That is ... 

The most popular method of data presentation is that of cumulative frequency. An example of this is shown as follows ... 

FIGURE 2. Effects of d-amphetamine and methysergide on the cumulative frequency of attack hites and sideways threats (top) and walking duration (bottom) during the initial and later resident-intruder confrontations... 

The FREQ Procedure ae Frequency Percent Cumulative Frequency Cumulative Percent... 

A typical testing procedure involves several steps. First, the selected number and size of sieves are stacked upon one another, with the largest openings (inversely related to mesh per inch) being at the top of the stack, and beneath that a pan to collect the particles finer than the smallest sieve. The known amount of powder to be analyzed is then placed on the top sieve and the set is vibrated in a mechanical device for a predetermined time period. The results are obtained by weighing the amount of material retained on each sieve and on the collecting pan. The suction method uses one sieve at a time and examines the amount retained on the screen. In both methods the data are expressed as frequency or cumulative frequency plots, respectively. 

Frequency domain performance, involving comparison of cumulative frequency distributions of the observed data and model predictions. In many situations, considering the various sources of error discussed earlier, it may... 

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