EXAMPLE 3.2.11
The annual
earnings for employees of a certain restaurant are given below:
12 laborers earn
$8000 each.
10 laborers earn
$9000 each.
4 supervisors
earn $11000 each
The
owner/manager earns $240,000.
Of the three
measures of central tendency, which will be the least accurate representation
of "typical earnings?"
SOLUTION
In this
distribution, n = 27.
The mode is
$8000, since that value has the greatest frequency.
The median is
the 14th number in the ordered list. Since the first 12 numbers are
all Ò8000sÓ and the next 10 numbers are all Ò9000s,Ó the median (the 14th
number) is $9000.
The mean is the
sum of all 27 numbers, divided by 27:
= 17,407.41
The mean is
$17,407.41. This is not a very
good indication of the typical earnings, since only one of the 27 people earns
at least that much. This is
another example of how the mean can be distorted by the presence of an extreme
value.