5 Further Exercises

Exercise 1

The file "NHSScotland.txt" contains data on the number of patients attending A&E every month in each of the 14 Scottish NHS boards, from 2007 up to 2023. This data set has the following variables:

  • "Date": the end of the month that patient numbers are aggregated over.
  • "NHSBoard": the Scottish NHS board the patients are from.
  • "TotalAttendances": the total number of patients attending A&E in a given month and NHS board.
  • "Within4Hours": the number of patients whose wait time was less than 4 hours.
  • "Over4Hours": the number of patients whose wait time was greater than 4 hours.
  • "Over8Hours": the number of patients whose wait time was greater than 8 hours.
  • "Over12Hours": the number of patients whose wait time was greater than 12 hours.

    1. Read "NHSScotland.txt" into R and save it as a data frame called nhs.

    2. Change the column "NHSBoard" to be a factor. (Hint: you can see the names of all the Scottish NHS boards using the code unique(nhs$NHSBoard).)

    3. Add an additional column to nhs which calculates the percentage of total patients in A&E whose wait time is less than 4 hours. Call this new variable "PercentageWithin4Hours".

    4. What is the average percentage of patients who had to wait less than 4 hours in each of the 14 Scottish NHS boards? (Hint: think how you can use the tapply() function.)

    1. Create a new data frame, called glasgow, which is a subset of nhs. This data set should only show observations from NHS Greater Glasgow & Clyde, as well as only having the variables "Date", "TotalAttendances" and "Over4Hours".

    2. Sort glasgow in order of decreasing number of patients who had to wait more than 4 hours in A&E. When did the greatest number of patients have to wait for longer than 4 hours?

  3. The file "HBPopulation.csv" contains data relating to the population size (in 2021) of each of the 14 Scottish NHS boards. Read this file into R and save it as a data frame called population. Merge nhs and population so that A&E attendance and the health board population size can be seen in the same data frame.

Exercise 2

Draw a random sample of 100 values from the \(\mbox{Poisson}(3)\) distribution and save these in a vector x.

If any of these random values are less than 3, use a for loop containing an if statement, to change these value to be equal to 3.

Exercise 3

The volume of a cylinder is calculated as \(V_{\mbox{cylinder}}=\pi r^2h\) where \(r\) is the radius of the cylinder and \(h\) is the height.

  1. Write a function called cyl.vol which takes the arguments r and h and returns the volume of cylinder with radius r and height h.

    Use your function to find the volume of a cylinder with which has radius 2.8cm and height 24cm.

  2. Use your function cyl.vol to write another function which can be used to calculate the total volume of \(n\) cylinders of the same size. This second function should take the arguments r for the radius, h for the height and n for the number of cylinders.