Download Chapter 2 - Psychology at Illinois State University

Chapter 2
Central Tendency & Variability
Tues. Aug. 27, 2013
Measures of Central Tendency The
Mean
• Sum of all the scores divided by the number of
scores
M 
X
N
• Mean of 7,8,8,7,3,1,6,9,3,8
– ΣX =
– N = 10
– Mean (or M) =
The Mode
• Most common single number in a distribution
• Mode of 7,8,8,7,3,1,6,9,3,8?
• Measure of central tendency for nominal
variables (most common category was…)
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 here
– ? How do we decide between using mean or median?
The Median
• With large data sets, shortcut…
– If odd N, divide by 2, then add ½, gives position of
the median score in list.
• Ex?
– If even N, divide by 2, this and score above it need
to be averaged for median.
• ex?
Example of Mean/Median Preference
• Evolutionary psych example in book (p. 40-41) – competing
theories of gender diffs in how many mates we prefer
– Buss (evol.) – men should prefer more partners than
women (to spread genes)
– Miller – men/women should prefer same #
• Table 2-1, data from 106 men, 160 women
• Women’s M=2.8, Median = 1, Mode = 1
• Men’s M=64.3, Median = 1, Mode = 1
• See Fig 2-8, how do outliers affect the mean in this study?
Median?
Location of Mean, Mode, Median
Measures of Spread
The Variance
• The average of each score’s squared difference
from the mean
• Steps for computing the variance:
1. Subtract the mean from each score
2. Square each of these deviation scores
3. Add up the squared deviation scores
4. Divide the sum of squared deviation
scores by the number of scores
Measures of Spread
The Variance
• Formula for the variance:
SD
2

2
(X

M)

SD=Standard Deviation
(when squared = variance)
N
SS- Sum of
Squares
SS

N
What variance tells us
• Conceptually, it is the average of the squared
deviation scores, so…
– The more spread out the distribution, the larger the
variance
• What if variance = 0?
– Very important for many stat tests
– Conceptual difference in unit of variance versus
standard deviation?
• Which is more intuitive?
Measures of Spread
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
• Conceptually, it is the average of deviations from the
mean.
– How much do most scores differ from the mean?
Measures of Spread
The Standard Deviation
• Formula for the standard deviation:
SD 
SD
2

 (X
 M)

N
2
SS
N
SD Computational Formula:
• Easier to use w/large data sets
• Uses sum of x scores (X) and sum of squared
x scores (X2)
• SD2 = X2 – [(X)2 / N]
N
• Note that your book prefers the definitional
formula, not this one
• p. 51 – some instances when we divide SS by
N-1