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Chapter 2 Measures of Location and Spread
Markov's Inequality (for lists)
If the mean of a list of numbers is
M
, and the list contains no
negative number then
[fraction of numbers in the list that are greater than or equal to x] ≤
M
/x.
Chebychev's inequality (for lists)
If the mean of a list of numbers is
M
and the standard deviation of
the list is SD, then for every positive number
k
,
[the fraction of numbers in the list that are
k
×
SD
or further from
M
] ≤ 1/
k
2
.
Estimating using the Regression Line
For regressing Y on X, (estimate of Y in standard units) =
r
×(measured X in standard units)
For regressing X on Y, (estimate of X in standard units) =
r
×(measured Y in standard units).
Residual plots can reveal computational errors
A residual plot shows at a glance whether the regression line was
computed correctly.
If the regression line was computed correctly, the point of averages
of the residual plot will be on the
x
axis, and the residuals will not
have a trend: the correlation coefficient for the residuals and X will
be zero.
If the residuals have a trend, the slope of the regression line was
miscalculated.
If the residuals do not have a trend, but the average of the residuals
is not zero, the intercept of the regression line was miscalculated.
If the residuals have a trend and the average of the residuals is not
zero, the slope of the regression line was miscalculated, and the
intercept of the regression might also have been miscalculated.
Permutations
The number of possible permutations (orderings) of
k
of
n
things is
n
P
k
=
n
!/(
n

k
)!
(
k
must be at least 0 and no larger than
n
.)
Combinations
The number of possible combinations of
n
things taken
k
at a time
(without regard to order) is
n
!
n
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 Summer '08
 anderes
 Statistics, Probability

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