# R Dataset / Package HistData / Cavendish

Webform
Category

Webform
Category

Webform
Category

Webform
Category

Webform
Category

Webform
Category

## Visual Summaries

Embed
<iframe src="https://embed.picostat.com/r-dataset-package-histdata-cavendish.html" frameBorder="0" width="100%" height="307px" />
Attachment Size
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 command-line 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 Earth

### Description

Henry 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.

### Usage

data(Cavendish)

### Format

A 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

### Details

Density 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.

density contains Cavendish's measurements as analyzed, where he treated the value 4.88 as if it were 5.88. density2 corrects this. Cavendish also changed his experimental apparatus after the sixth determination, using a stiffer wire in the torsion balance. density3 replaces the first 6 values with NA.

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.

### Source

Kyle 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, 1055-1098

### References

Cavendish, H. (1798). Experiments to determine the density of the earth. Philosophical Transactions of the Royal Society of London, 88 (Part II), 469-527. 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.

### Examples

data(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.

Picostat Manual
###### How To Register With a Username
1. Go to the user registration page.
4. Click Submit.
5. Click the link that was sent to the email address you registered with.
6. Clicking the link will open another page on Picostat where you can select a password.
7. Click Save and enter any profile details you wish to enter.
###### How To Register With Google Single Sign On (SSO)
1. Go to the user login page.
5. Google will redirect you back to Picostat with your new account created and you will be logged in.
6. Enter any profile details you wish to share.
1. Go to the user login page.
3. Click "Login". You will be redirected to your user homepage authenticated.
1. Go to the user login page.
3. If you already registered with Picostat via Google SSO, you will be redirected to your user homepage authenticated.
###### How To Import a Dataset
1. Create a Picostat account or login with your existing picostat account (see above).
2. Go to the dataset import page.
3. Select a license for the dataset. The default is "No License" but allows Picostat to host a copy of the dataset as per the privacy policy. You may wish to uncheck the "Public" option if you do not wish to share your dataset with others. R Datasets that come by downloading R have a GNU General Public License v3.0 which may also be selected from the Picostat dropdown.
4. Enter a title for the dataset
5. Choose a dataset input methods. Available options include:
• Random data - this populates your dataset with random numbers between 0 and 100. You can specify the number of rows and columns for the random dataset.
• CSV, TSV or TXT file - you will have the option upload a file within the current file size limit and also specify the header and whether or not the dataset is a contingency table. With contingency tables, the first column becomes a label for the rows. Currently with Picostat, there is limited support for contingency tables. Choose "Yes" to the Header option if the first line of the data contains titles for the rows. Also choose the Separator for the dataset. A separator is what breaks the data up. In some cases, a comma would separate data values in a row. You will also have the option to add documentation in the form keyboarded text and also uploaded documentation attachments. You can also specify a license for the documentation.
• Copy and Paste. This selection contains many of the same fields as importing a file with an additional textarea to copy and paste data to.
• Empty dataset. Start with a blank dataset and manually add data with the Picostat dataset editor.
• Excel file - Choose this option if you would like to convert your Excel spreadsheet to a Picostat dataset. With this selection, you will have the option to specify whether to use the first row in the Excel file as column names. If you would like to choose a specific sheet to use, you can also specify with entering its name in the text input.
• sas7bdat file - SAS is a powerful statistical software package that has its own proprietary file format. Choose this option if you are importing a SAS file.
• SPSS sav file - SPSS is a statistical package owned by IBM. You can import SPSS files by choosing this option.
6. Choose whether or not the dataset contains a header. Some of the dataset input methods allow you to specify whether or not a Header exists on the file. Sometimes dataset files contain a Header as the first row which names the columns. If you choose "Yes" to this, the first row in the dataset will become column headers.
7. You can also add documentation and specify a documentation license. This can be used to help explain your dataset to those unfamiliar with it.
8. Choose whether or not to upload an supporting attachments.
9. Pass the captcha. To prevent spam submissions, Picostat has a captcha which is used to prevent automated submissions by bots.
10. Choose a privacy setting for the dataset. You can also specify whether or not the dataset is Public. If you uncheck this setting, only you and the Picostat administrator will be able to view the dataset.
11. Submit the form. Once the form is validated, you will be redirected to the dataset homepage where you can choose to edit or perform statistical operations on the dataset.
###### How To Perform Statistical Analysis with Picostat
1. Go to any dataset homepage. You can get a full list at the dashboard.
2. Near the top of the page there will be two drop downs. One for analysis and one for education. Here we will choose Analyis. Choose from one of the following:
• Numerical Summaries - Here you can get the:
1. Arithmetic mean
2. Median
3. Quartiles
4. Minimum and Maximum
5. Stem-and-leaf plot
6. Standard deviation and Variance
7. IQR
8. Cumulative frequencies
• Plot - a plot of two columns on the cartesian coordinate system
• Boxplot - a Boxplot (box-and-whisker plot) of a column.
• Correlation Coefficient - Compute the correlation coefficient between two columns.
• Cumulative Frequency Histogram - Display a cumulative frequency histogram
• Dotplot
• Hollow Histogram - Plot two columns on the same histogram with a different color for each column.
• Pie Chart
• Regression - Perform a simple linear regression and compute the p-value and regression line. Also plots the data with the regression line.
• Stem and Leaf Plots - Plot a one or two-sided stem-and-leaf plot from one or two columns respectively.
• Visual Summaries - plots the following:
1. Frequency Histogram
2. Relative Frequency Histogram
3. Cumulative Frequency Histogram
4. Boxplot (Box-and-whisker plot)
5. Dotplot
3. PDF - Check this box if you want to download a PDF of the output from the statistical analysis application.
4. HTML - Check this box if you want a link to the HTML page created with the application.
5. R File - Check this box if you want a link to download the R commands used to generate output from this statistical application. You should be able to copy the commands verbatim into R Studio or R to recreate the analysis.
###### How To Use Educational Applications with Picostat
1. Go to any dataset homepage. You can get a full list at the dashboard.
2. Near the top of the page there will be two drop downs. One for analysis and one for education. Here we will choose Education. Choose from one of the following:
• How To Create a Barplot - This will show you how to create a bar chart after selecting a column with the mouse.
• How To Create a Stacked Barplot - This application will show you how to create a stacked bar plot from a column vector.
• How To Create a Pie Chart - This application will show you how to create a pie chart from a column of data
• How To Compute the Mean - This application will show you how to compute the mean from a column vector
• How To Create a Plot - This app will show you how to plot two columns in the cartesian coordinate system.
• How To Compute the Media - This statisistical app will show you how to compute the median from a column vector.
3. PDF - Check this box if you want to download a PDF of the output from the education application.
4. HTML - Check this box if you want a link to the HTML page created with the application.
Recent Queries For This Dataset

No queries made on this dataset yet.

Title Authored on Content type
R Dataset / Package datasets / sunspot.year March 9, 2018 - 1:06 PM Dataset
R Dataset / Package datasets / airmiles March 9, 2018 - 1:06 PM Dataset
R Dataset / Package Stat2Data / SampleFG March 9, 2018 - 1:06 PM Dataset
OpenIntro Statistics Dataset - toy_anova August 9, 2020 - 2:38 PM Dataset
swiss February 26, 2017 - 11:28 AM Dataset