The preceding problem demonstrated the calculation of a sample mean. We knew it was a
sample because the five values of interest were taken from a population of 100. We could have
computed the mean of all 100 dollar amounts. In such a case we would have had a population
mean. The difference between a sample mean and a population mean is that the population
mean includes every value in the population; whereas the sample mean includes only a portion of
the values in the population. The population mean is still the sum of the values of interest divided
by the number of values of interest. Now we are interested in the entire population.
Even though they are computed in the same manner they are different concepts and we will
need a different symbol for each. The symbol for population mean is the Greek letter u
(pronounced mu). The formula for the population mean is
u = ΣX
X still represents each value of interest. However, we are now interested in all values in the
N represents the number of items of interest in the population. Note this is a capital N rather
than the small n used in the sample mean formula.
For example, suppose the number of calculator batteries used during all ten 3-week courses
held this year is 37, 62, 28, 31, 58, 29, 35, 47, 52, and 25. We need to know the average number
of batteries used in a 3-week course this year.
a. Find the mean. __________________
b. Is this a sample or a population mean? __________________