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Standard Deviations

Data Set A is a normally distributed data set that has a 95

percentile value of 6 seconds,

an 85

percentile value of 5 seconds, and a maximum value of 7 seconds. In this case,

reporting either the 85

or 95

percentile values represents the data in a manner where

the assumptions a stakeholder is likely to make about the data are likely to be appropriate
to the data.

Medians

A median is simply the middle value in a data set when sequenced from lowest to
highest. In cases where there is an even number of data points and the two center values
are not the same, some disciplines suggest that the median is the average of the two
center data points, while others suggest choosing the value closer to the average of the
entire set of data. In the case of the exemplar data sets, Data Sets A and B have median
values of 4, and Data Set C has a median value of 1.

Normal Values

A normal value is the single value that occurs most often in a data set. Data Set A has a
normal value of 4, Data Set B has a normal value of 3, and Data Set C has a normal value
of 1.

Standard Deviations

By definition, one standard deviation is the amount of variance within a set of
measurements that encompasses approximately the top 68 percent of all measurements in
the data set; in other words, knowing the standard deviation of your data set tells you how
densely the data points are clustered around the mean. Simply put, the smaller the
standard deviation, the more consistent the data. To illustrate, the standard deviation of
Data Set A is approximately 1.5, the standard deviation of Data Set B is approximately
6.0, and the standard deviation of Data Set C is approximately 2.6.

A common rule in this case is: "Data with a standard deviation greater than half of its
mean should be treated as suspect. If the data is accurate, the phenomenon the data
represents is not displaying a normal distribution pattern." Applying this rule, Data Set A
is likely to be a reasonable example of a normal distribution; Data Set B may or may not
be a reasonable representation of a normal distribution; and Data Set C is undoubtedly
not a reasonable representation of a normal distribution.

Uniform Distributions

Uniform distributions sometimes known as linear distributions represent a
collection of data that is roughly equivalent to a set of random numbers evenly spaced
between the upper and lower bounds. In a uniform distribution, every number in the data
set is represented approximately the same number of times. Uniform distributions are
frequently used when modeling user delays, but are not common in response time results
data. In fact, uniformly distributed results in response time data may be an indication of
suspect results.