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.