Quibans 97: Curious coronavirus cases

This Quibans uses the first part of an article from the Bristol Post, published on Weds 21 October 2020. I intend to use this a bit at a time, asking questions and revealing the next part of the article after each answer. My answers are at the end.



Part 1:

Bristol University coronavirus cases nearing 1,100 as more staff members test positive

The number of staff members to have tested positive for coronavirus at the University of Bristol has more than doubled in a week, latest figures show.

Question 1) The focus here is on the number of members of staff who have tested positive. What percentage of the 1,100 do you guess are staff and what percentage are students?




Part 2:

A total of 1,050 students have tested positive for covid-19 at the University of Bristol 

Q2) Now you have got some additional information, calculate the percentage of the cases that are staff and that are students.



Part 3:

A total of 1,050 students have tested positive for covid-19 at the University of Bristol now, together with 19 members of staff, taking the total of confirmed cases at the university to 1,079 - a daily rise of 67 positive tests.

Q3) Any comments?

Q4) What is the actual percentage of cases that are staff and students?



Part 4:

In recent days, the number of new positive tests among students seems to have slowed down and Tuesday saw the biggest rise in six days (83) as the University hadn't confirmed that many positive tests among its students since last Wednesday, October 14, when 126 cases were confirmed. However, the number of positive tests among staff members now seems to be rising quickly, having more than doubled since last Wednesday when eight coronavirus cases were confirmed among university staff.

Q5) What is the percentage increase for staff over the week?

Q6) If the staff cases continue to increase at the same rate, in which week will the number of staff cases reach 1000?

Q7) Why is this unlikely to happen?



Part 5:

Belowis a graph from the article.

Q8) How does it work?

Q9) Work out the numbers for some of the orange bars and blue dots.

Q10) What criticisms do you have of the graph?

Q11) Why is Oct 19 lower?

 





Answers:

1) It doesn’t really matter what the class suggest; the reason for doing this is that they will very likely get a percentage for the staff that is vastly too low.

2) Presumably that means 50 staff and 1050 students, so 4.5% are staff and 95.5% are students.

3) The numbers don’t add up! 1050 students plus 19 members of staff equals 1069 and not 1079. And the headline says “nearing 1,100”, which is a rounded version of 1069.

4) 19/1069 gives a staff percentage of 1.8%, with 98.2% of the cases being amongst students. This focus on staff seems less than important!

5) Last week it was 8 and now it’s 19, so the multiplier is 19/8 = 2.375, so the increase is 1.375, which is a 137.5% increase.

6) Keep multiplying the number of staff cases by 2.375

After 1 week: 19 x 2.375 = 45.125 (It might appear that we should round this to 45, but it’s not going to be an exact increase, so I am not particularly bothered about using 45.125)

After 2 weeks: 45.125 x 2.375 = 107.171875

After 3 weeks: 107.171875 x 2.375 = 255

After 4 weeks: 605

After 5 weeks: 1436

We could have done this by using 2.3753, etc. 

7) 1000 staff would be a considerable fraction of the staff of the university, whereas 1050 students is tiny compared to the number of students. It seems unlikely that this figure will be reached for staff. The student figure is declining after only a few days, so a sustained increase over 5 weeks seems unlikely.

8) It appears that the scale for the yellow bars is on the left hand side, while the scale for the blue dots is on the right hand side. The horizontal lines work for the left hand scale; you have to look very carefully at the tiny marks next to the numbers on the right hand scale.

The first day has 119 cases (the blue dot) and after that the height of the yellow bar is added to the previous day’s blue dot to get the next blue dot.



Q9) If you go to the graph on the website you can hover over the bars and dots to see the actual numbers.



Q10) Plenty of criticisms!

Why doesn’t the right hand scale start at zero? Starting at 100 doesn’t save very much space!

What happened to Oct 8, 10 and 11 ? Given that the blue dots (for the total number of cases) matches up with the yellow bars that have been added on, does that mean about half of the cases shown for Oct 9 were really from Oct 8? How would the graph look different if Oct 8, 10, 11 were included too?


Q11) It seems odd to have Oct 19 being so much lower and the day after much bigger again. Oct 19 was a Monday. The graph shows when cases were confirmed, so presumably this is 24 or 48 hours after the students were given a covid test. It might be that fewer people were tests on 17 or 18 Oct (because it was a weekend).

Source: https://www.bristolpost.co.uk/news/bristol-news/bristol-university-coronavirus-cases-nearing-4627979