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From Figure 10.1, roughly what are the upper and lower quartiles and the median of the distribution of melting points?

From Figure 10.1, roughly what are the upper and lower quartiles and the median of the distribution of melting points?

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
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ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
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From Figure 10.1, roughly what are the upper and lower quartiles and the median of the distribution of melting points?
Transcribed Image Text:From Figure 10.1, roughly what are the upper and lower quartiles and the median of the distribution of melting points?
As an example of the use of the ecdf, let us consider data taken from a study by White, Riethof, and Kushnir (1960) of the chemical properties of beeswax. The aim of the study was to investigate chemical methods for detecting the presence of synthetic waxes that had been added to beeswax. For example, the addition of microcrystalline wax raises the melting point of beeswax. If all pure beeswax had the same melting point, its determination would be a reasonable way to detect dilutions. The melting point and other chemical properties of beeswax, however, vary from one beehive to another. The authors obtained samples of pure beeswax from 59 sources, measured several chemical properties, and examined the variability of the measurements. The 59 melting points (in °C) are listed here. As a summary of these measurements, the ecdf is plotted in Figure 10.1. 63.78 63.45 63.58 63.08 63.40 64.42 63.27 63.83 63.10 63.34 63.50 63.83 63.63 63.27 63.30 63.50 63.36 63.86 63.34 63.92 63.88 63.36 63.36 63.51 63.51 63.84 64.27 63.43 63.50 63.56 63.39 63.78 63.92 63.92 63.56 64.21 64.24 64.12 63.92 63.53 63.50 63.30 63.86 63.93 63.43 64.40 63.61 63.03 63.68 63.13 63.41 63.60 63.13 63.69 63.05 62.85 63.31 63.66 63.60 1.0- 62.8 63.2 63.6 64.0 64.4 Melting point ("C) FIGURE 10.1 The empirical cumulative distribution function of the melting points of beeswax. Figure 10.1 conveniently summarizes the natural variability in melting points. For example, we can see from the graph that about 90% of the samples had melting points less than 64.2°C and that about 12% had melting points less than 63.2 C. White, Riethof, and Kushnir showed that the addition of 5% microcrystalline wax raised the melting point of beeswax by .85°C and the addition of 10% raised the melting point by 2.22 C. From Figure 10.1, we can see that an addition of 5% microcrystalline wax might well be difficult to detect, especially if it was made to beeswax that had a low melting point, but that an addition of 10% would be detectable. In further calculations, the investigators modeled the distribution of melting points as Gaussian. How reasonable does this model appear to be? Cumulative frequency
Transcribed Image Text:As an example of the use of the ecdf, let us consider data taken from a study by White, Riethof, and Kushnir (1960) of the chemical properties of beeswax. The aim of the study was to investigate chemical methods for detecting the presence of synthetic waxes that had been added to beeswax. For example, the addition of microcrystalline wax raises the melting point of beeswax. If all pure beeswax had the same melting point, its determination would be a reasonable way to detect dilutions. The melting point and other chemical properties of beeswax, however, vary from one beehive to another. The authors obtained samples of pure beeswax from 59 sources, measured several chemical properties, and examined the variability of the measurements. The 59 melting points (in °C) are listed here. As a summary of these measurements, the ecdf is plotted in Figure 10.1. 63.78 63.45 63.58 63.08 63.40 64.42 63.27 63.83 63.10 63.34 63.50 63.83 63.63 63.27 63.30 63.50 63.36 63.86 63.34 63.92 63.88 63.36 63.36 63.51 63.51 63.84 64.27 63.43 63.50 63.56 63.39 63.78 63.92 63.92 63.56 64.21 64.24 64.12 63.92 63.53 63.50 63.30 63.86 63.93 63.43 64.40 63.61 63.03 63.68 63.13 63.41 63.60 63.13 63.69 63.05 62.85 63.31 63.66 63.60 1.0- 62.8 63.2 63.6 64.0 64.4 Melting point ("C) FIGURE 10.1 The empirical cumulative distribution function of the melting points of beeswax. Figure 10.1 conveniently summarizes the natural variability in melting points. For example, we can see from the graph that about 90% of the samples had melting points less than 64.2°C and that about 12% had melting points less than 63.2 C. White, Riethof, and Kushnir showed that the addition of 5% microcrystalline wax raised the melting point of beeswax by .85°C and the addition of 10% raised the melting point by 2.22 C. From Figure 10.1, we can see that an addition of 5% microcrystalline wax might well be difficult to detect, especially if it was made to beeswax that had a low melting point, but that an addition of 10% would be detectable. In further calculations, the investigators modeled the distribution of melting points as Gaussian. How reasonable does this model appear to be? Cumulative frequency
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