to work out the average distance of travel of the company’s staff. When Georgina
drew a histogram of results the distribution showed no particular form, but at
least she could calculate the average distance travelled.
Georgina’s histogram of distance travelled by her colleagues to work
This average turned out to be 20 miles. Mathematicians denote this by the
Greek letter mu, written μ, and so here μ, = 20. The variability in the population
is denoted by the Greek letter sigma, written σ, which is sometimes called the
standard deviation. If the standard deviation is small the data is close together
and has little variability, but if it is large, the data is spread out. The company’s
marketing analyst, who had trained as a statistician, showed Georgina that she
might have got around the same value of 20 by sampling. There was no need to
ask all the employees. This estimation technique depends on the Central Limit
Theorem.
Take a random sample of staff from all of the company’s workforce. The
larger the sample the better, but 30 employees will do nicely. In selecting this
sample at random it is likely there will be people who live around the corner and
some long-distance travellers as well. When we calculate the average distance for
our sample, the effect of the longer distances will average out the shorter
distances. Mathematicians write the average of the sample as , which is read as
‘x bar’. In Georgina’s case, it is most likely that the value of will be near 20, the
average of the population. Though it is certainly possible, it is unlikely that the
average of the sample will be very small or very large.