Copyright 2004Dr. J. Kyle Roberts
University of North Texas
Unit 1: Background to Inferential Statistics
Lesson 2: Measures of Central Tendency
EDER 6010: Statistics for Educational Research
Dr. J. Kyle Roberts
University of North Texas
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Copyright 2004Dr. J. Kyle Roberts
University of North Texas
Three Measures of Central Tendency
Mode
Median
Mean
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Copyright 2004Dr. J. Kyle Roberts
University of North Texas
ModeThe value in a distribution of scores that occurs the most frequently
X
9
8
8
6
5
7
8
X f
9 1
8 3
7 1
6 1
5 1
Mode = 8
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Copyright 2004Dr. J. Kyle Roberts
University of North Texas
ModeQuestion 1 Can I have more than one mode?
X
9
8
8
6
5
7
7
X f
9 1
8 2
7 2
6 1
5 1
X
1
2
3
4
5
Question 2 Must I have a mode?
Question 3 What level of scale do I need to compute a mode?
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Copyright 2004Dr. J. Kyle Roberts
University of North Texas
What Good is a Mode Anyway?
What do I know if I know that the mode of my dataset is 5?
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Copyright 2004Dr. J. Kyle Roberts
University of North Texas
MedianThe “Middle” Score
The median is the score that divides the distribution of scores into two equal halves
Odd numbers of people Even numbers of people
2
nX Lowest
X
1
2
3
4
5
221 MiddleMiddle XX X
1
2
3
4Mdx=3 Mdx=2.5
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Copyright 2004Dr. J. Kyle Roberts
University of North Texas
What Good is a Median Anyway?
What do I know if I know that the median of my dataset is 5?
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Copyright 2004Dr. J. Kyle Roberts
University of North Texas
MeanThe “average” score
n
XX i
Y
TAASX
GRE
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Copyright 2004Dr. J. Kyle Roberts
University of North Texas
Computing the Mean
X
1
2
3
4
5
5
54321 X
5
15X
3X
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Copyright 2004Dr. J. Kyle Roberts
University of North Texas
What Good is a Mean Anyway?
What do I know if I know that the mean of my dataset is 5?
Next Slide
Copyright 2004Dr. J. Kyle Roberts
University of North Texas
Questions about Central Tendency!! X
1
3
2
2
3
5
2
What would the mode of this dataset be?
a. 1b. 2c. 3d. 4e. 5
a. 1b. 2c. 3d. 4e. 5
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Copyright 2004Dr. J. Kyle Roberts
University of North Texas
Questions about Central Tendency!! X
1
3
2
2
3
5
2
What would the median of this dataset be?
a. 1b. 2c. 3d. 4e. 5
a. 1b. 2c. 3d. 4e. 5
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Copyright 2004Dr. J. Kyle Roberts
University of North Texas
Questions about Central Tendency!! X
1
3
2
2
3
5
2
What would the mean of this dataset be?
a. 1.50b. 2c. 2.57d. 3.8e. 18
a. 1.50b. 2c. 2.57d. 3.8e. 18
7
2532231 X
7
18X
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Copyright 2004Dr. J. Kyle Roberts
University of North Texas
Unit 1: Background to Inferential Statistics
Lesson 2: Measures of Central Tendency
EDER 6010: Statistics for Educational Research
Dr. J. Kyle Roberts
University of North Texas
