Fermi Estimation
… Fermi estimation is a type of rough and ready calculation that aims to get a reasonable estimate to problem when not much direct information is known.
… The essential part of any fairly estimation is to state your assumptions (estimated values) clearly. You won’t be judged on whether your assumptions are correct!
… You will be using multiplication and division when making a Fermi estimate.
… To help you form reasonable starting assumptions, use upper and lower bound estimates and then take a mean.
… Here is an example of the steps in a Fermi estimate of the number of piano tuners in Liverpool (!)… Note that you should use upper and lower bounds where possible to help you find a mean.
a) Population of Liverpool?… About 2 million (smaller than Birmingham, Manchester so would need to find out these approximate numbers)
b) Number in a family?… Upper bound 6, lower bound 1… So say 4
c) Number of households?… Use a) and b)
2,000,000 ÷ 4 = 500,000 households
d) Proportion of households with a piano?… Say upper bound of 2 in 50 and a lower bound of 0 in 50, so estimate 1 in every 50 households
e) Number of pianos in Liverpool?… Use answers c) and d):
500,000 x 1/50 = 10,000 pianos
f) How often would a household get their piano tuned?… Say once per year
g) How many pianos can one piano tuner tune per day?… Upper bound of 4, lower bound of 0, so say 2 pianos/day.
h) How many pianos can one piano tuner tune per year?… Use g) and a 5-day working week with 50 weeks in the year:
2 x 5 x 50 = 500 pianos/year
i) Use answers e) and h) to estimate the number of piano tuners in Liverpool:
10,000 ÷ 500 = 20 piano tuners in Liverpool!
PHEW!
Here are some more Fermi estimates to try:
The number of times your heart has beaten since birth.
The number of secondary schools in the UK.
The number of Smarties needed to fill a double-decker bus!
Sampling Methods
… Four methods of taking a sample of data from a population are:
Random
Cluster
Stratified
Quota
How do each of these methods work and what are their advantages and disadvantages?
… A census is where every item in the population is surveyed.