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Welcome to MM570
Applies Statistics for
Psychology
Unit 2 Seminar
Dr. Bob Lockwood
Measures of Central Tendency:
The Mean
• Sum of all the scores divided by the
number of scores
• Mean of 7,8,8,7,3,1,6,9,3,8
• ΣX = 7+8+8+7+3+1+6+9+3+8 = 60
• N = 10
• Mean = 60/10 = 6
The Mean
Mean of the
distribution of
the number of
dreams during
a week for 10
students.
Measures of Central Tendency:
The Mode
• Most common single number in a distribution
• Mode of 7,8,8,7,3,1,6,9,3,8 = 8
• Measure of central tendency for nominal
variables
The Mode
The mode as the high point in a distribution’s
histogram, using the example of the number of dreams
during a week for 10 students.
Measures of Central Tendency:
The Median
• The middle score when all scores are
arranged from lowest to highest
• Median of 7,8,8,7,3,1,6,9,3,8
• 1336778889
median
• Median is the average (mean) of the 5th and
6th scores, so the median is 7
Measures of Central Tendency
Types of Data
Measure of Central Tendency
Type of Data
Mode Median Mean
Nominal
Yes
No
No
Ordinal
Yes
Yes
No
Equal Interval* Yes
Yes
Yes
Ratio*
Yes
Yes
Yes
 SPSS refers to these as Scale data. The reason is based on this table, in terms of
statistical analyses; there is no difference between equal interval and ratio data.
Measures of Variability:
The Variance
• The average of each score’s squared
difference from the mean
• Steps for computing the variance:
1.
2.
3.
4.
Subtract the mean from each score
Square each of these deviation scores
Add up the squared deviation scores
Divide the sum of squared deviations
by the number of scores
Measures of Variability:
The Variance
• Formula for the variance:
Measures of Variability:
The Standard Deviation
• Most common way of describing the
spread of a group of scores
• Steps for computing the standard
deviation:
1. Figure the variance
2. Take the square root
[Hint: I use SPSS]
Measures of Variability:
The Standard Deviation
• Formula for the standard deviation:
Table 2-4: Figuring the Variance and Standard Deviation for
Number of Social Interactions during a week for 94 College
Students (page 48)
Number of Interactions
48
15
33
--35
9
30
8
26
-
Mean number of
Interactions
=
Deviation
Score
Squared Deviation
Score
-
17.39
17.39
17.39
=
=
=
30.16
-2.39
15.61
936.97
5.71
243.67
-
17.39
17.39
17.39
17.39
17.39
=
=
=
=
=
17.61
-8.39
12.61
-9.39
8.61
∑: 0.00
310.11
70.39
159.01
88.17
74.13
∑: 12,406.44
Controversies and Limitations:
The Tyranny of the Mean
• Knowledge about the individual case is lost when
taking averages
• Qualitative research methods
• e.g., case studies, ethnography
Using SPSS Mean, Median, Mode,
Variance and Standard Deviation
Enter the scores in one column of the Data Window
  Analyze
  Descriptive Statistics
  Frequencies
  the variable you want to make a frequency table of
  the arrow, then  Statistics
  Mean, Median, Mode, Variance, Standard Deviation
  Continue
  OK
SPSS Numerical Descriptors 1
SPSS Numerical Descriptors 2
SPSS Numerical Descriptors 3
SPSS Descriptive Statistics –
Descriptives
SPSS Descriptive Statistics –
Descriptives
SPSS Descriptive Statistics –
Descriptives
QUESTIONS??