R Dataset / Package HistData / Cavendish
Attachment  Size 

dataset80101.csv  447 bytes 
Documentation 

On this Picostat.com statistics page, you will find information about the Cavendish data set which pertains to Cavendish's Determinations of the Density of the Earth. The Cavendish data set is found in the HistData R package. Try to load the Cavendish data set in R by issuing the following command at the console data("Cavendish"). This may load the data into a variable called Cavendish. If R says the Cavendish data set is not found, you can try installing the package by issuing this command install.packages("HistData") and then attempt to reload the data with library("HistData") followed by data("Cavendish"). Perhaps strangley, if R gives you no output after entering a command, it means the command succeeded. If it succeeded you can see the data by typing Cavendish at the commandline which should display the entire dataset. If you need to download R, you can go to the R project website. You can download a CSV (comma separated values) version of the Cavendish R data set. The size of this file is about 447 bytes. Cavendish's Determinations of the Density of the EarthDescriptionHenry Cavendish carried out a series of experiments in 1798 to determine the mean density of the earth, as an indirect means to calculate the gravitational constant, G, in Newton's formula for the force (f) of gravitational attraction, f = G m M / r^2 between two bodies of mass m and M. Stigler (1977) used these data to illustrate properties of robust estimators with real, historical data. For these data sets, he found that trimmed means performed as well or better than more elaborate robust estimators. Usagedata(Cavendish) FormatA data frame with 29 observations on the following 3 variables.
DetailsDensity values (D) of the earth are given as relative to that of water. If the earth is regarded as a sphere of radius R, Newton's law can be expressed as G D = 3 g / (4 π R), where g=9.806 m/s^2 is the acceleration due to gravity; so G is proportional to 1/D.
The modern "true" value of D is taken as 5.517. The gravitational constant can be expressed as G = 6.674 * 10^11 m^3/kg/s^2. SourceKyle Siegrist, "Virtual Laboratories in Probability and Statistics", http://www.math.uah.edu/stat/data/Cavendish.html Stephen M. Stigler (1977), "Do robust estimators work with real data?", Annals of Statistics, 5, 10551098 ReferencesCavendish, H. (1798). Experiments to determine the density of the earth. Philosophical Transactions of the Royal Society of London, 88 (Part II), 469527. Reprinted in A. S. Mackenzie (ed.), The Laws of Gravitation, 1900, New York: American. Brownlee, K. A. (1965). Statistical theory and methodology in science and engineering, NY: Wiley, p. 520. Examplesdata(Cavendish) summary(Cavendish) boxplot(Cavendish, ylab='Density', xlab='Data set') abline(h=5.517, col="red", lwd=2)# trimmed means sapply(Cavendish, mean, trim=.1, na.rm=TRUE)# express in terms of G G < function(D, g=9.806, R=6371) 3*g / (4 * pi * R * D) boxplot(10^5 * G(Cavendish), ylab='~ Gravitational constant (G)', xlab='Data set') abline(h=10^5 * G(5.517), col="red", lwd=2)  Dataset imported from https://www.rproject.org. 
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