Unformatted text preview: 9  7.5 = 1.5 More measures of Variability
v༇ Range Largest minus smallest measurement: max – min. v༇ Variance The “average” of the squared deviations of all the measurements from the mean. v༇ Standard Deviation (SD) The square root of the variance. SD is the most
common measure of spread or variability. Relationship: SD = Variance
Notation: Variance = s2, SD = s. Idea of Variance and SD
v༇ How far away are the observations, on average, from the mean?
v༇ Based on the deviations xi − x = Difference between ith observation and mean
n 1
2
s=
∑ ( xi − x )
n − 1 i =1
2 “average” squared deviation Example: SD Calculation
5 data point corresponding to variable X: x1 = 1, x2 = 2, x3 = 3, x4 = 4, x5 = 5 x1 + x2 + x3 + x4 + x5
x=
= 3.
5 s=? Example: SD Calculation
xi x 1 3 xi − x ( xi − x) 2
2 4 2 3 1 1 3 3 0 0 4 3 1 n=5
n −1 = 4 10
s=
4
2 1 5 3 2
_____ 4
______ 0 10 = 2.5
s = 2.5 ≈ 1.58. SD Calculation: More practice
100, 100, 100, 100, 100, 100, 100 s = ? 90, 90, 90, 100, 110, 110, 110 s = ? SD: Interesting details
v༇ Why SQUARE?
q༇ Sum of deviations (not squared) is just 0. Squaring the
deviations converts the negative deviations to positive
numbers.
q༇ SD is a natural measure of spread for an important class of
distributions: the normal distributions (we will cover later). v༇ Why divide by n1 and not n?
q༇ It’s unimportant if n is large.
q༇ Dividing by n...
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This note was uploaded on 01/15/2014 for the course BUAD 310 taught by Professor Lv during the Fall '07 term at USC.
 Fall '07
 Lv

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