Download Measures of Dispersion

Measures of Dispersion
Range
(Stat5_Dispersion)
The range is the max minus the min.
Range = max − min
Standard Deviation and Variance
The standard deviation is a "kind of" average distance of the scores from the mean. The
Variance is the standard deviation squared.
Value
34
28
26
26
22
20
156
-
Mean
26
26
26
26
26
26
Value - Mean
Mean = 156 = 26
Deviation (Deviation)^2
6
8
64
2
4
Variance = 120 = 20
0
0
6
0
0
Square root of the Variance is
Std Dev = 4.47
-4
16
-6
36
NOTE:
0
120
<--Sums
Sample Standard
Deviation
2
STEPS:
(
x − x)
∑
1) Find the mean
s=
n −1
2) Subtract the mean from each score (value) to get the deviations
Sample Variance is s 2
3) Square the deviations
2
4) Add the squares of the deviations
s
=
s
5) Divide the sum by the number of scores to get the variance
6) Take the square root of the variance to get the standard deviation
*NOTE: Relating the standard deviation to the "average distance of the scores from the mean"
•
The standard deviation may be thought of as a "kind of", "average distance of the scores from the
mean" (for intuitive purposes).
Suppose the mean is 50 and a student gets a 45. Then their score is 5 from the mean. Another
student gets a 43. Then their score is 7 from the mean. We continue this process and compute the
sum of all these distances. We then divide by the number of distances giving an average distance.
Although this average distance in not the same as the standard deviation, it is in the "ballpark". Hence,
the standard deviation may be thought of the "average distance of the scores from the mean" (for
intuitive purposes).
Last printed 3/29/02 7:01 AM
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Created on 7/18/98 8:25 PM Last printed 3/29/02 7:01 AM R Mower, Instructor