8-3 Statistics: Range and Standard Deviation
 statisticians need to know what the central tendency of a
set of scores is: mean, median
 they also want to know how “spread out” the scores are
 statistics that measure the spread are called measures of
dispersion
RANGE
The range of a set of scores is the distance from lowest to
highest score: range = (high score – low score)
STANDARD DEVIATION
 the most commonly used measure of dispersion
 notation (for the whole population):  (“sigma”)
 notation (for a sample): s
Here’s the formula for s, the sample standard deviation
 of a set of n scores: x1, x2, x3, … , xn
 with sample mean: x
n
2
 ( xi  x )
s=
i 1
n 1
 why will data that is more “spread out”
 give a larger standard deviation?
8-3
p. 1
 A distribution with “large” standard deviation:
-100
100
0
One with “small” standard deviation:
-20
8-3
0
20
p. 2