Information Technology Reference
In-Depth Information
Left-Skewed
Symmetric
Mean = Median = Mode
Right-Skewed
Median
Mean
Mean
Median
Mode
FIGURE 6.5
Symmetric and skewed distribution.
spread because it is understood so easily. However, it is very sensitive to extreme
scores because it is based on only two values. The range should almost never be used
as the only measure of spread, but it can be informative if used as a supplement to
other measures of spread such as the standard deviation and interquartile range. For
example, the range is determined for the following “ y ” sample as follows:
[10
,
12
,
4
,
6,13,15,19
,
16]
R y
=
Max[10
,
12
,
4
,
6,13,15,19
,
16]
Min[10
,
12
,
4
,
6,13,15,19
,
16]
=
19
4
=
15
(6.1)
The range is a useful statistic to know but not as a stand-alone dispersion measure
because it takes into account only two scores.
The variance is a measure of the spreading out of a distribution. It is computed
as the average squared deviation of each number from its mean. Formulas for the
variance are as follows.
For a population:
i = 1 y i µ y 2
N
N
2
y
σ
=
(6.2)
where N is the number of population observations
For a sample:
i = 1 ( y i
n
y ) 2
s y =
(6.3)
n
1
where n is the sample size
The standard deviation is the measure of dispersion most commonly used. The
formula for the standard deviation is the square root of the variance. An important
 
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