Question $1.$ The following items require you to use the $$mtcars$$ dataset in R$.$ To find out the field names and units of measurement, type $?$ mtcars$$ into the R console. $(6$ marks$)$

What is the average miles per gallon for all vehicles in the mtcars database $(1$ marks$)?$

What is the standard deviation of the number of cylinders for all vehicles in the mtcars database $(1$ marks$)?$

If you were to choose a measure of central tendency for the gross horsepower across all vehicles in the mtcars database, would you choose the mean or the median? Why?

$(2$ marks$)$

If you were to choose a measure of variability for the displacement in cubic inches across all vehicles in the mtcars database, would you choose the standard deviation or the interquartile range? Why? $(2$ marks$)$

Question $2.$ The following items require you to use the $$Orange$$ dataset in R$.$ To find out the field names and units of measurement, type $?$ Orange$$ into your R console. $(6$ marks$)$

Create a scatterplot of the relationship between tree age and the trunk circumference in millimetres of all trees in the Orange database. To copy$/$paste it into Word, click $$Export$$ above the plot in your R viewer, click $$Copy to Clipboard$,$ and then click $$Copy Plot$.$ You may then paste it into Word. $(3$ marks$)$

Describe the relationship presented in your plot in the following terms and justify your answer: $(3$ marks$)$

Is the relationship positive, negative, or is there no relationship?

Is the relationship linear or non$-$linear?

Is the relationship weak, moderate, or strong?

Question $3.$ The following items require you to use the table to the right.

$(6$ marks$)$

Create a proportion table from a vector that shows the proportions of all four majors shown at right. Report the proportions as percentages and round them out to two decimal places. $(2$ marks$)$

Create a coloured stacked bar plot that shows the proportions of each major split by gender. Follow the instructions in $2$a$.$ above to copy and paste your chart into Word. $(2$ marks$)$

Without performing further analysis, describe your observations of the differences in majors between men and women. What do you see when you look at this plot? $(2$ marks$)$

Sex Major

Male Psychology

Male Physics

Male Psychology

Male Biology

Male Chemistry

Male Biology

Male Biology

Male Physics

Female Physics

Female Biology

Female Physics

Female Psychology

Female Chemistry

Female Physics

Female Psychology

Female Biology