Descriptive Intervals

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Descriptive Intervals
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Computation

• First, edit and summarise the data. Obtain the
  sample mean (m) and sample standard
  deviation(sd).
• Compute the short interval as lower m-2sd
• And upper m 2sd. Write the interval as
  lower,upper.
• Compute the long interval as lower m-3sd
• And upper m 3sd. Write the interval as
  lower,upper.

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Interpretive Base Tchebysheffs Inequalities

• At least 75 of the sample points reside within
  the short interval
• At least 89 of the sample points reside within
  the long interval
• In general, at least (1-(1/k2))100 of the
  sample points reside within the interval
  m-ksd,mksd.

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The Bell Curve Assumption

• In probability we have a family of populations
  that follow a Gaussian or Bell Curve Assumption.
• These populations have a super-majority of
  members residing near a central value, with
  population density declining symmetrically as the
  distance from the central value grows. If one
  plots population density versus location, the
  resulting shape resembles a bell.

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The Gaussian distribution When many independent
random factors act in an additive manner to
create variability, data will follow a
bell-shaped distribution called the Gaussian
distribution, illustrated in the figure below.
The left panel shows the distribution of a large
sample of data. Each value is shown as a dot,
with the points moved horizontally to avoid too
much overlap. This is called a column scatter
graph. The frequency distribution, or histogram,
of the values is shown in the middle panel. It
shows the exact distribution of values in this
particular sample. The right panel shows an ideal
Gaussian distribution. Ref. link
http//www.graphpad.com/articles/interpret/princip
les/gaussian.htm
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Center
Center
Center
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Interpretive Base Empirical Rule

• When the data for our intervals come from a
  bell-shaped population, then
• Approximately 95 of the sample points reside
  within the short interval
• Approximately 100 of the sample points reside
  within the long interval