Download Chapter 3 Summary Statistics: Measures of Location and Spread

Chapter 3 Summary Statistics:
Measures of Location and Spread
Other Measures of Location:
The Median and the Mode
prepared by David Herzig
The Median
Sample data

Test Scores
100
90
80
70
60
50
40
30
20
10
0
1
2
3
4
5
6
7
Student
Test Score
1
78
2
79
3
83
4
83
5
87
6
92
7
95
The Median
Student
Test Score
1
78
2
4
5
6
7
79
83
83
87
92
95
median
3
3 values
The value of a set
of ordered
observations that
has an equal
number of
observations above
and below it.
3 values

The Median

The value of a set
of ordered
observations that
has an equal
number of
observations above
and below it.
Test Scores
3 values
3 values
100
90
80
70
60
50
40
30
20
10
0
1
2
3
median
4
5
6
7
The Median

Determination

For an odd number of observations, the
median is the middle observation of the
set, as shown in our initial example.

For an even number of observations, the
median is the average of the two middle
observations of the set.
The Median
Student
Test Score
1
67
2
75
3
83
4
87
5
88
6
94
Median =
83 + 87
2
=
85
The Mode

The value of the
observations that
occurs most
frequently in the
sample.
Student
Test Score
1
78
2
79
3
83
4
83
5
87
6
92
7
95
mode
The Median and The Mode

Uses

Describe the location of data best when
the distributions of observations cannot
be fit to a standard probability
distribution.

Or when there are extreme observations
The Median
The Relationship between Skew and Central Tendency
If NORMAL curve
Mean = median = mode
If POSITIVELY SKEWED
curve
mean > median > mode
If NEGATIVELY SKEWED
curve
mode > median > mean