MATH10002 - Intro to Statistics

Workshop 1: Descriptive Statistics – Minitab

NAME:

Student Number:

This sheet should be completed and made available for checking at the end of the class so that you can receive credit for attendance.

The First Fleet

Under the command of Captain Arthur Phillip of the Royal Navy, eleven ships carrying over 1400 persons sailed from Portsmouth on 13 May 1787. Bound for Botany Bay in the colony of New South Wales, Australia, the First Fleet covered over 15,000 miles in eight months. Six transports (Alexander, Charlotte, Friendship, Lady Penrhyn, Prince of Wales, Scarborough) carried the 778 convicts while three store ships provided supplies and two men-o-war carrying the official party protected the fleet. The conditions were very difficult and thirty seven lives were lost en route.

The data for this workshop are taken from, “The Crimes of the First Fleet Convicts” by John Cobley, Angus & Robertson Publishers, Australia, 1970. It is stored in the Minitab worksheet called firstfleet.mtw to be found in the folder :

\\uk-ac-man-ss7\vol3\shared\eps\Maths\MATH10002

This directory corresponds to eps\Maths\MATH10002 in the "Shared data" area on the CLIP image

The data set contains detailed information on 778 convicts. We may regard these data as a sample of all those convicts transported to Australia from the UK in the latter half of the 18th century. As such, we may be able to infer something about the characteristics of all convicts transported to Australia at this time.

1. Open Minitab. To do this on a PC in the AlanTuringBuilding cluster, firstly open the Start menu. Then select All Programs > Site Licenced Applications > Statistics > Minitab 15.1 Once Minitab has opened you can retrieve the information on the First Fleet convicts by clicking on File > OpenWorksheet and selecting the file firstfleet.mtwat the above location. The data set contains information on twelve variables listed below:

Variable Description

  • SNAME The family name commonly used
  • GNAME The given first name of the convict.
  • SEX Either male or female.
  • SHIP The ship on which the convict was transported
  • DATE The date of the convict's trial, in the form month/day/year.
  • PLACE The area in England where the trial took place.
  • CRIME The crime for which the convict was transported.
  • VALUE The value of the crime in the year 1787 in shillings
  • SENT Either sentenced to Transportation or sentenced to death, but commuted to transportation
  • TERM The number of years to be spent as a convict.
  • TRADE The former trade of the convict.
  • AGE The age of the convict in 1787, if known.

The data for each variable is in a separate column of the worksheet. Please note that the symbol * in a cell of the worksheet indicates that the corresponding data value is missing and unknown.

2. Click on Stat > Tables > Tally and select gname for Variables. Click on OK, and have a look at the output. What were the most common male and female names in Britain in the mid-eighteenth century? Write down the three most common boys names and the three mostcommon girls names. What were some of the more unusual names?

3. Obtain the frequencies for sex. What were the numbers of male and female convicts sent? What percentage of the convicts weremale and what percentage were female? To do this you will need to select both Counts and Percents in the Tally dialog box. Show the resultsgraphically using Graph > Bar Chart.

4. Obtain the frequencies (tallies) and percentages (percents) for sentence. by sex using Stat > Tables > Cross Tabulation. Produce a bar chart of your results using Graph > Bar Chartand comment on your findings.

5. The variables crime and trade havemany categories. What were the five most common crimes committed? What were the five most populartrades?

6. The convicts were transported in six ships. Did some ships carry men and others women, or were thetransports mixed? To examine the relationship between ship and sexuseStat > Tables > Cross Tabulation. What do the results tell you? Some unusual observations areindicated in the table. Locate two of these unusual observations. Can you suggest any explanation?

7. Now look at the relationship between sex and sentence.. What sentence was a femaleconvict on the First Fleet most likely to receive? What percentages of women had received a death sentence? What percentage of convicts receiving death sentences werewomen?

Also, use cross tabulation to examine the relationship between sex and trade, and between sex and crime. Write afew sentences to summarize your findings.

8. Obtain numerical summary information about the ages of the convicts using Stat > Basic Statistics > DisplayDescriptive Statistics, selecting age for Variables. Obtain a histogram of age usingGraph > Histogram. Also, obtain a boxplot for age using Graph > Boxplot. Use these numerical and graphical summaries to describe the distribution of age.

Also, ‘outliers’ are unusual observations, often along way from the rest of the data and sometimes a result of mistakes in recording or entering the data. Whatoutliers appear to be in the data? Do you think they are actual mistakes?

9.Obtain descriptive statistics for the variable age for the male and thefemale convicts using Stat > Basic Statistics > DisplayDescriptive Statistics. For Variables enter age, tick by variable, click inside the box to the right and thenenter sex. Click on OK.

Also, produce boxplots for the male and female ages using Graph > Boxplot. Write a brief summary of your findings.

10. The variable value gives the value of the crime in shillings . (A shilling was one of the coins in the English currency of the time – there were twenty shillings in one pound.) Investigate this variable: first find its average value and its standard deviation and also a five number summary. Then have a look at its distribution with a histogram and a boxplot. Write a few sentences summarizing theresults.

Obtain descriptive statistics for value bysentence received and summarize your findings. Do you think that the value of a crime in eighteenth-centuryEngland influenced the sentence the criminal received?

Note. At the end, if you want to save a copy of your Minitab project (the contents of all the windows, including the columns of data in the worksheet(s), the stored constants and matrices in the worksheet(s), the complete text in the session window and history folder, as well aseach graph window) use File > Save Project As. Youwill be prompted for a filename which you should enter. Choose a location on your p-drive or memory stick so that you then have the options, at a later date, of resuming your session if you have not finished, examining your results in more detail and printing your results either directly from Minitab or after first copying and pasting selected parts into a Microsoft Word document. The project will be saved as a MPJ file. To reopen it later you double click on the icon of the saved file, but you must be using a computer with Minitab 15 installed on it.

If you wish, you can install a free, fully working, 30 day trial version of Minitab 15 on your own computer from the Minitab website at: