Chapter 3 Summary Statistics: Measures of Location and Spread

1
Chapter 3 Summary Statistics Measures of
Location and Spread

• Other Measures of Location The Median and the
  Mode
• prepared by David Herzig

2
The Median

• Sample data

Student Test Score
1 78
2 79
3 83
4 83
5 87
6 92
7 95
3
The Median

• The value of a set of ordered observations that
  has an equal number of observations above and
  below it.

3 values
median
3 values
4
The Median

• The value of a set of ordered observations that
  has an equal number of observations above and
  below it.

3 values
3 values
median
5
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.

6
The Median
Student Test Score
1 67
2 75
3 83
4 87
5 88
6 94
Median 83 87 2
85
7
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
8
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

9
The Median
The Relationship between Skew and Central Tendency The Relationship between Skew and Central Tendency
If NORMAL curve Mean median mode  
If POSITIVELY SKEWED curvemean gt median gt mode
If NEGATIVELY SKEWED curvemode gt median gt mean