9/1/2011
2
Example
•The set:
2,
9,
1,
5,
6
n
x
x
i
6
.
6
5
33
5
6
5
11
9
2
If we were able to enumerate the whole
population, the
population mean
would be
called
m
(the Greek letter ―
mu
‖).
• The
median
of a set of measurements
is the middle measurement when the
measurements are ranked from
smallest to largest.
• The
position of the median
is
Median
.5(
n
+ 1)
once the measurements have been
ordered.
Example
• The set:
2, 4, 9, 8, 6, 5, 3
n =
7
• Sort:
2, 3, 4, 5, 6, 8, 9
• Position:
.5(
n
+ 1) = .5(7 + 1) = 4
th
Median = 4
th
largest measurement
• The set:
2, 4, 9, 8, 6, 5
n =
6
• Sort:
2, 4, 5, 6, 8, 9
• Position:
.5(
n
+ 1) = .5(6 + 1) = 3.5
th
Median = (5 + 6)/2 = 5.5 — average of the 3
rd
and 4
th
measurements
Mode
• The
mode
is the measurement which
occurs most frequently.
• The set:
2, 4, 9, 8, 8, 5, 3
–The mode is
8
, which occurs twice
• The set:
2, 2, 9, 8, 8, 5, 3
–There are two modes—
8
and
2
(
bimodal
)
• The set:
2, 4, 9, 8, 5, 3
–There is
no mode
(each value is unique).