Histograms or Frequency Plots

Enll, W. E., Ehrlich, R. and Kennedy, S., Optimal definition of class intervals of histograms or frequency plots . In Morphological Analysis, Particle Characterisation in Technology (J. K Beddow, Ed.), Vol. II, Chap. II, CRC Press Inc., Boca Raton, EL (1984)... 

Pareto charts Run charts Control charts Planned experimentation Histograms or frequency plots Forms for collecting data Scatter plots... 

A modification of the histogram display of differences is a plot suggested by Krouwer and Mont)P Icnown as the mountain plot. This is a plot of cumulative frequencies (c/%) of differences up to 50% with subsequent subtracted cumulative frequencies (100% - cf%). Such a plot shows in principle the same information as a histogram or frequency polygon plot. An advantage may be that the percentiles can be directly read from the plot. 

These ten results represent a sample from a much larger population of data as, in theory, the analyst could have made measurements on many more samples taken from the tub of low-fat spread. Owing to the presence of random errors (see Section 6.3.3), there will always be differences between the results from replicate measurements. To get a clearer picture of how the results from replicate measurements are distributed, it is useful to plot the data. Figure 6.1 shows a frequency plot or histogram of the data. The horizontal axis is divided into bins , each representing a range of results, while the vertical axis shows the frequency with which results occur in each of the ranges (bins). 

As AD is made smaller, a histogram becomes a frequency distribution curve (Fig. 4.1) that may be used to characterize droplet size distribution if samples are sufficiently large. In addition to the frequency plot, a cumulative distribution plot has also been used to represent droplet size distribution. In this graphical representation (Fig. 4.2), a percentage of the total number, total surface area, total volume, or total mass of droplets below a given size is plotted vs. droplet size. Therefore, it is essentially a plot of the integral of the frequency curve. 

In Chapter 10 we saw that there are various methods for the analysis of categorical (and mostly binary) efficacy data. The same is true here. There are different methods that are appropriate for continuous data in certain circumstances, and not every method that we discuss is appropriate for every situation. A careful assessment of the data type, the shape of the distribution (which can be examined through a relative frequency histogram or a stem-and-leaf plot), and the sample size can help justify the most appropriate analysis approach. For example, if the shape of the distribution of the random variable is symmetric or the sample size is large (> 30) the sample mean would be considered a "reasonable" estimate of the population mean. Parametric analysis approaches such as the two-sample t test or an analysis of variance (ANOVA) would then be appropriate. However, when the distribution is severely asymmetric, or skewed, the sample mean is a poor estimate of the population mean. In such cases a nonparametric approach would be more appropriate. 

What The frequency plot (or histogram) is a tool to display data. It presents to the user basic information about the location, shape, and spread of a set of data. The frequency plot is similar to the Pareto chart. The frequency plot displays quantitative data, while the Pareto chart displays categorical data. 

A histogram or cumulative frequency plot will show what proportion of measurements exceed the criteria to show the extent of high corrosion risk. Where the ASTM criteria do not apply they will show the distribution of readings so that high risk areas can be identified. 

Data are analyzed by flow cytometry analysis software (BD FACS Diva, BD Biosciences Flowjo, TreeStar). Data presentation using the frequency of positive events is appropriate only in presence of a bimodal distribution of the emitted fluorescence. In this case, there is no particular preference for the use of the histogram or the dot plot to present data. In case of a non-bimodal distribution of the emitted fluorescence, data should be reported as relative MFI (i.e., the ratio between the MFI values of the sample stained with aU the experimental markers and the MFI values of the negative control sample) and the histogram layout should be preferred. Differently from frequency data, this analytical approach provides relative quantitative information of the chemokine receptor expression levels on the surface of each... 

Histogram (frequency plot)—a graphical tool used to understand variability. The chart is constructed with a block of data separated into 5 to 12 bars or sections from low number to high number. The vertical axis is the frequency and the horizontal axis is the "scale of characteristics." The finished chart resembles a bell if the data is in control. 

The check sheet shown below, which is tool number five, is a simple technique for recording data (47). A check sheet can present the data as a histogram when results are tabulated as a frequency distribution, or a mn chart when the data are plotted vs time. The advantage of this approach to data collection is the abiUty to rapidly accumulate and analy2e data for trends. A check sheet for causes of off-standard polymer production might be as follows ... 

When X represents a continuous variable quantity, it is sometimes convenient to take the total or relative frequency of occurrences within a given range of x values. These frequencies can then be plotted against the midvalues of x to form a histogram. In this case, the ordinate should be the frequency per unit of width x. This makes the area under any bar proportional to the probability that the value of x will he in the given range. If the relative frequency is plotted as ordinate, the sum of the areas under the bars is unity. 

One underlying principle of classical statistics is that any observation in nature has an uncertainty associated with it. One extension of this principle is that multiple observations of the same object will result in a distribution of values. One common graphical representation of a distribution of values is the histogram, where the frequency of occurrence of a value is plotted versus the value. Many statistical tools are based on a specific type of distribution, namely the Gaussian, or Normal distribution, which has the following mathematical form ... 

Another way in which these kinds of data are sometimes represented is as a cumulative curve in which the total number (or fraction) of particles nT>, having diameters less (sometimes more) than and including a particular d, are plotted versus dr Figure 1.18b shows the cumulative plot for the same data shown in Figure 1.18a as a histogram. The cumulative curve is equivalent to the integral of the frequency distribution up to the specified class mark. Cumulative distribution curves are used in Chapter 2 in connection with sedimentation. 

Example 1.2 A coarsely ground sample of com kernel is analyzed for size distribution, as given in Table El.3. Plot the density function curves for (1) normal or Gaussian distribution, (2) log-normal distribution, and (3) Rosin-Rammler distribution. Compare these distributions with the frequency distribution histogram based on the data and identify the distribution which best fits the data. 

For longitudinal modes, we can therefore stale that the number of modes with frequency less than a> is 2 w/waY atom-pair, or a density of modes of 6w lwy, modes per atom-pair per frequency-range. Similarly, construct the spectrum for transverse modes and plot the total on the same abscissa as in Fig. 9-6 so that comparison can be made. (That histogram did not have a normalized scale on the ordinate, so you need not worry about the ordinate.) The principal discrepancies are understandable by comparison of the Debye approximation to the spectrum shown in Fig. 9-2. 

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