Information Technology Reference
In-Depth Information
±
3σ
99.73%
±
2σ
95.45%
±
σ
68.27%
µ
FIGURE 6.6
Normal distribution curve.
attribute of the standard deviation is that if the mean and standard deviation of a
normal distribution are known, it is possible to compute the percentile rank associated
with any given observation. For example, the empirical rule states that in a normal
distribution, approximately 68.27% of the data points are within 1 standard deviation
of the mean, approximately 95.45% of the data points are within 2 standard deviations
of the mean, and approximately 99.73% of the data points are within 3 standard
deviations of the mean. Figure 6.6 illustrates the normal distribution curve percentage
data points contained within several standard deviations from the mean.
The standard deviation often is not considered a good measure of spread in highly
skewed distributions and should be supplemented in those cases by the interquartile
range (Q
3
-Q
1
). The interquartile range rarely is used as a measure of spread because
it is not very mathematically tractable. However, it is less sensitive to extreme data
points than the standard deviation, and subsequently, it is less subject to sampling
fluctuations in highly skewed distributions.
For the data set shown in Table 6.4, a set of descriptive statistics, shown in Table
6.5, is computed using a Microsoft Excel (Microsoft Corporation, Redmond, WA)
sheet to summarize the behavior of
y
=
“Usage” data in Table 6.4.
6.4
INFERENTIAL STATISTICS
Inferential statistics are used to draw inferences about a population from a sample on
n
observations. Inferential statistics generally require that sampling be both random
and representative. Observations are selected by randomly choosing the sample that
resembles the population's functional requirement. This can be obtained as follows:
1. A sample is random if the method for obtaining the sample meets the criterion of
randomness (each item or element of the population having an equal chance of
Search WWH ::
Custom Search