# R Dataset / Package HistData / Cavendish

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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. You can load the Cavendish data set in R by issuing the following command at the console data("Cavendish"). This will 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. 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 Earth## DescriptionHenry 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,
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. `density` Cavendish's 29 determinations of the mean density of the earth `density2` same as `density` , with the third value (4.88) replaced by 5.88`density3` same as `density` , omitting the the first 6 observations
## 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
The modern "true" value of D is taken as 5.517.
The gravitational constant can be expressed as ## 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 ## ReferencesCavendish, H. (1798). Experiments to determine the density of the earth.
Brownlee, K. A. (1965). ## 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.r-project.org. |

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Attachment | Size |
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dataset-80101.csv | 447 bytes |