CIS2300_TEST1
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Population
 a collection of persons, objects or items of interest.
 Whatever the researcher is studying

parameter
 a descriptive measure of the population. Usually denoted by Greek letters
 e.g. mean(µ), population variance(σ^2), populuation standard deviation(σ)

sample
a portion of the whole and if taken properly, representative of the whole

statistic
 a descriptive measure of the sample. Usually denoted by Roman letters
 e.g. mean(x *bar*), sample variance (s^2), sample standard deviation(s)

Descriptive Statistics
 Using data gathered on a group to describe or reach concclusions about that same group
 e.g. most athletic stats. The data is gathered from that group and conclusions are drawn about that group only. Basketball stats are about Basketball

Inferential Statistics
 gathering data from a sample and use the statistics generated to reach conlusions about the population from which the sample was taken
 sometimes referred to as inductive statistics

emprical rule
 The approximate values that lie within a given number of standard deviations from the mean of a set of data if the data are normally distributed.
 Distance from the Mean Values within Distance
 µ + 1σ 68%
 µ + 2σ 95%
 µ + 3σ 99.7%

Population Mean
 µ = (∑x)/N
 where x = actual data values
 N = # total terms

standard deviation
 square root of the variance
 σ = sqrt(σ)
 Σ = sqrt( (∑(x µ)^2)/N)

sum of squares of x
 SSx
 The sum of the squared deviations about the mean of a set of values

variance
 average of the squared deviations about the arithmetic mean for a set of numbers
 Population Variance
  σ^2 = (∑(x µ)^2)/N)

deviation from the mean
xµ

mean absolute deviation (MAD)
 the average of the absolute values of the deviations around the mean for a set of numbers
 MAD = (∑xµ)/N
 where
 xµ = actual value of a given number minus the mean
 N= Number of terms

Chebyshev's Theorem
 at least (11/k^2) values will fall within + k standard deviations of the mean regardless of the shape of the distribution. Assume k>1
 e.g. k=2.5, 11/(2.5^2) = .84. so at least .84 of all values are within µ + 2.5σ.
 or at least .84 of all values will be within 2.5 standard deviations of the mean, µ.

sample variance
 variance: s^2 = ∑(x x(bar))^2)/(n1)
 also
 s^2 = (∑x^2  ((∑x)^2)/n)/n1
 where
 x = actual value
 x(bar) = sample mean
 n = sample number

sample standard deviation
 sqrt(s^2) where s^2 =
 s^2 = (∑x^2  ((∑x)^2)/n)/n1