a
:
1, 4, 8, 14, 20
[
n
+1]/2= 6/2= 3
The third observation is the median.
The median is 8.
b
:
1, 4, 8, 14, 20, 21
[
n
+1]/2= 7/2= 3.5
The median is the average of the third and fourth observations.
The median is 11.
c
:
1, 4, 8, 14, 20, 100
[
n
+1]/2=7/2= 3.5
The median is the average of the third and fourth observations.
The median is 11.
The strength of the median is that it is a resistant measure of center:
it is resistant to the
influence of a few extreme observations.
In the example above, note that increasing the
maximum value significantly from
b
to
c
did not change the median at all.
The Mode
The mode
is the number that occurs most frequently in a set of data values.
x
:
80, 90, 90, 100
The mode is 90.
Measures of Spread
While we care about measures of center, we also care about measures of spread.
For
instance, median income might be the same in country
A
and country
B
.
If, however,
everyone has the same income in country
A
while there is extreme inequality in country
B
, then country
A
and country
B
are very different countries.
The Range