Frequency histograms

Fig. 4. Frequency histogram of data in categories I and II for variable where V = variance (14).

Due to its nature, random error cannot be eliminated by calibration. Hence, the only way to deal with it is to assess its probable value and present this measurement inaccuracy with the measurement result. This requires a basic statistical manipulation of the normal distribution, as the random error is normally close to the normal distribution. Figure 12.10 shows a frequency histogram of a repeated measurement and the normal distribution f(x) based on the sample mean and variance. The total area under the curve represents the probability of all possible measured results and thus has the value of unity. 

The experimental sample on which the frequency histogram is based has an experimental mean m and an experimental variance s, which are... 

Bulk particulates of various sizes can be analysed to display their particle size distribution and a frequency histogram plotted, as shown in Figure 1.8. 

The first step in data analysis is the selection of the best filling probability function, often beginning with a graphical analysis of the frequency histogram. Moment ratios and moment-ratio diagrams (with p as abscissa and as ordinate) are useful since probability functions of known distributions have characteristic values of p, and p. ... 

Figure 1.17. Frequency histogram for the Ag content of electrum from Kuroko deposits in Japan (Shikazono...

Figure 1.34. Frequency histogram for MgO/FeO ratios (in wt%) of chlorite from the basalt studied (A) and MORE (B). Data sources are Shikazono and Kawahata (1987), Humphris and Thompson (1978) (M Mid-Atlantic Ridge) and Kawahata (1984) (C Costa Rica Rift, Galapagos Spreading Centre). The data on chlorite from MORE are taken from typical metabasalt and not from quartz-chlorite breccia and veins which formed in a hydrothermal upflow zone (Shikazono et al., 1987).

Figure 1.107. Frequency histogram for S C of type-A(a) and type B (b) carbonates (Shikaz.ono, 1989).

A frequency histogram of the Ag content of electrum from epithermal gold-silver vein-type deposits and the Tsugu deposit (Fig. 1.174) clearly indicates that the Au/Ag of electrum from the Tsugu deposit is higher than that from epithermal vein-type deposits. 

Fig. 21.8. Frequency histograms of single-channel conductances for (A) SENS and (B) LEVR parasites. Gaussian curves were fitted to each distribution using the maximum likelihood procedure. The peaks for the SENS isolate were 21.4 + 2.3 pS (8% area) labelled G25 33.0 + 4.8 pS (31% area) labelled G35 38.1 + 1.2 pS (19% area) labelled G40 and 44.3 + 2.2 pS (42% area) labelled G45. The peaks for the LEVR isolate were 25.2 4.5 pS (21% area) labelled G25 41.2 1.7 pS (49% area) labelled G40 and 46.7 1.1 pS (30% area) labelled G45.

This protocol describes one of several useful procedures for constructing DNA content frequency histograms that yield information about cell-cycle phase distributions. The method uses ethanol-fixation to prepare cells for staining with PI. 

Set up the flow cytometer to acquire red fluorescence signals as pulse width and pulse area (integral) values, so that doublets can be discerned and gated out before analyzing the DNA content frequency histogram (see Wersto et al., 2001, for a discussion of the doublet discrimination procedure). 

Analyze the data (as in O Figure 13-7) by using DNA content frequency histogram deconvolution software, such as ModFit LT (Verity Software, Inc., Topsham, ME). 

Draw frequency histograms at intervals of 0.1 for the data in Problems 3.1 and 3.2. Calculate the variance and standard deviation for each of the two sets of data. 

The multivariate techniques which reveal underlying factors such as principal component factor analysis (PCA), soft Independent modeling of class analogy (SIMCA), partial least squares (PLS), and cluster analysis work optimally If each measurement or parameter Is normally distributed In the measurement space. Frequency histograms should be calculated to check the normality of the data to be analyzed. Skewed distributions are often observed In atmospheric studies due to the process of mixing of plumes with ambient air. 

Figure 1 taken from the petroleum industry shows a quality control chart where the data in the frequency histogram is normally distributed. In this particular control chart, the grand average is 7.08 and is surrounded by + 1, 2, 3 standard deviations rather than range values. 

Normative data using 40-min trials terminated after sleep onset have been published with extrapolations to estimate results if 20- and 30-min trials had been used. Figure 2 is a frequency histogram and Table 1 is a summary of parameters for normative MWT data gathered in the international, multisite cooperative... 

Figure 2 Nonnative MWT data. Average sleep latencies over four 40-min long MWT trials were calculated for each of 64 healthy volunteers and plotted in frequency histogram format. (See text and Ref. 11 for details.)...

Figure 6 Frequency histogram for time of day of motor vehicle crashes and fall-asleep attacks on the PVT. The open bars represent the 60-min frequency of 4333 crashes in which the driver was judged to be asleep but not intoxicated across the 24-hr day and the solid bars represent fall-asleep attacks (failure to respond for 30 sec on the PVT) in n = 14 subjects, measured at 120-min intervals across 42 hr of total sleep deprivation. Both the fatigue-related crashes and fall-asleep attacks follow an equivalent temporal profile across the day, with occurrences increasing across the nocturnal period, and peaking between 07 00 and 08 00. (Adapted from Refs. 92 and 94.)...

Figure 4. Frequency histograms for combined estimates of , the rate of cross-fertilization, and F, the coefficient of inbreeding...

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