Average If all values were equal they would be this amount. Add all values
and divide by how many there are. Example: For 2,2,4,6,7,7,8 the
average is 36 / 7 = 5.14, rounded. The symbol is  ,"mu" for a population mean and  , "x bar" for a sample mean. Mean and average are the same.
Attribute data is information about qualities-- types of defects or information
like color or "strongly prefers". Attributes can not be ranked
or averaged. Data is either attribute or variable data.
Assignable cause or special cause Sources of variation which produce nonrandom
errors, which affect production in an identifiable way are assignable
causes. Wear on a saw blade causing it to cut a curved path is
an assignable cause. The slight variations in cut due to many
different, minute, and self canceling causes are not assignable
causes.
Bias A biased sample consistently misrepresents the population from
which it comes. Trying to find the average student shoe size by
measuring people in the gym would bias the result, probably toward
a larger average. Bias can be introduced by choices from a subset
of the population which shares a characteristic.
Capability A capable process consistently produces output that is within
specifications. To be consistent, a process must be in statistical
control. Capability may be determined only for a process that
is in statistical control. One measure of capability is the Cpk
ratio, the distance to the nearest specification limit divided
by 3 standard deviations. A desirable Cpk is 1.33.
Empirical rule The practical use of theoretical probabilities in normally distributed
data. For example, the empirical rule holds that in a normally
distributed population, 34% of the observations will fall within
one standard deviation above the mean.
Grand average The average of averages, symbolized by  , "x double bar," or "x bar The grand average is also equal to
the average of the x's.
Histogram A type of bar chart in which numerical data are grouped by size
and the count (frequency) of each size is shown by the length
of the bar. Histograms are charts of frequency tables.
Judgment sampling A sampling method in which samples are selected by taking items
that appear, in the judgment of the person taking the sample,
to be representative of the population.
Mean The same as the average.
Median The middle value of an ordered (sorted) list of values, or the
average of the middle two values if there is no single middle
value. Example: 2,2,4,6,7,7,8, the median is 6.
Mode The value that appears most often. There can be two modes. Example:
In 2,2,4,6,7,7,8, the modes are 2 and 7.
n The sample size. For the sample red, blue, green, red, black,
n = 5. See Sample.
Normal curve or normal distribution The bell curve governing many natural
and industrial processes, in which most values are clustered about
the mean, and fewer values away from the mean. The probability
of being near or far from the mean is determined by the empirical
rule.
Population The population is the universe of all possible values we want
information about. If the population is "all compact cars," measuring
the gas mileage for every car yields a population mean of 26.2
mpg (or = 26.2 mpg).
Proportion One meaning is part of a whole. The proportion of people who
are left-handed is approximately 0.11. Other ways of expressing
proportions are as a percent: 12.6% of men are left handed, or
as a rate: 99 per 1000 women are left handed. A proportion also
refers to equal ratios.
Random sample Every member of the population under study has an equal chance
of appearing in the sample. Random numbers are often used to pick
which subjects or items are included in the sample.
Sample A sample is a subgroup taken from a population. The number of
observations in a sample is represented by the letter n. In the
sample 7,6,2, n = 3. Samples are used to estimate characteristics
of populations (called parameters) where it is impractical to
measure all members of the population.
Sample mean The average of a group of values constituting a sample. Symbol
, "x bar". Example: Given 2,2,4,6,7,7,8 as the population, take
a sample of three values, randomly selected, 7,6,2. The sample
mean is the average of the three, or = 5.
Sort Sorted data is put in order. Consider the list 2, 4, 2, 4.5,
1, 3. The sorted values in ascending order are 1, 2, 2, 3, 4,
4.5. Spreadsheets and some calculators have commands for sorting
data.
Specification limits The tolerances set to determine acceptable product. Usually they
are maximum (upper specification limit) and minimum (lower specification
limit) measurements. Specification limits are usually set by design
considerations outside of the process, while control limits are
a result of the measurements within the process.
Standard deviation A number that measures the dispersion of a set of values about
their average. Its units are the same as the units of the values.
The symbol is  (sigma) for population standard deviation and s for sample standard
deviation. Their formulas differ slightly.
Statistical control A process is in statistical control when variation in the process
is not distinguishable from random background variation. The variation
is without pattern, and exhibits a normal distribution of values
about the mean.
Random A random sample is one in which each member of the population
has an equal chance of being picked. Random numbers can be used
to select samples which avoid human judgment bias.
Range The distance between the maximum and minimum observations. The
symbol for range is R. Example: the range of 2,2,4,6,7,7,8 is
8 - 2, so R = 6.
Variable data are numerical measurements used to distinguish amounts such as
diameters in millimeters or temperature. Variable data can be
ranked and averaged. Average age, average temperature and average
coating thickness are examples of variable data. Not all numerical
data is not variable data. Social security numbers are like names;
an average social security number of a group of people does not
have meaning.
Z score or standardized value. A value expressed in standard deviations.
Z = , where x is the value, is the mean, and is the standard deviation. 
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