Stat 101 Formulas Sample Statistics
Stat 101 Formulas
Sample Statistics
Sample mean
1 =
=1
Sample variance
2
=
1 -
1
(
-
)2
=
2
- 2 -1
=1
Sample standard deviation
=
2
=
1 -
1
(
-
)2
=1
5-Number summary
Range
0 = 1 = 1
2 = 3 = 3
4 =
= -
= 4 - 0
Inter-Quartile Range
= 3 - 1 Fences for Outliers
1 - 1.5 , 3 + 1.5
Simple Linear Regression
Sample Covariance
(,
)
=
- ( - 1)
Sample Correlation
=
(,
)
=
- ( - 1)
Regression Model
= +
Slope Intercept
=
= -
Residual
= - = - ( + )
Normal Distribution
Standardize Un-Standardize
- =
= +
68/95/99.7 Rule
(-1 < < 1) .68
(-2 < < 2) .95
(-3 < < 3) .997
kth Percentile
( < ) = %
Brian Powers, Summer 2014
Stat 101 Formulas
Probability
Complement Rule
() = 1 - ()
General Addition Rule
( ) = () + () - ( )
Multiplication Rule for Independent Events
( ) = () ()
General Multiplication Rule
( ) = () (|) = () ((|)
Conditional Probability
(|)
=
( ) ()
A and B are Independent if:
1) ( ) = () ()
2) () = (|)
3) () = (|)
Random Variables
Expected Value
= () = ( = ) =
Variance
=1
=1
2 = () = (( - )2) = (2) - 2 = ( - )2
Linearity of Expected Value
=1
() = () ( + ) = () + ( + ) = () + ()
Variance of a Linear Combination () = 2()
( + ) = () ( + ) = 2() + 2() + 2(, )
Variance of Linear Combination of Independent X,Y ( + ) = 2() + 2()
(1 + 2 + + ) = ()
Brian Powers, Summer 2014
Stat 101 Formulas
Special Distributions Bernoulli(p)
( = 1) = ( = 0) = = 1 -
() = () =
Binomial(n,p)
Sum of n independent Bernoullis
(
=
)
=
( )
-
=
(,
,
)
(
)
=
()
-
=
(,
,
)
=0
() =
() =
Central Limit Theorem
If
1,
...
,
independent,
come
from
a
distribution
with
mean
and
standard
deviation
approximately follows a Normal distribution with mean and standard deviation .
Sampling Distributions (assuming CLT applies)
If x1,...,xn ~Bernoulli(p)
~(, ) (, )
=
~
(,
)
If x1,...,xn ~ have mean and standard deviation
~(, )
=
~
(,
)
Confidence Intervals
(1-)100% Confidence Interval
Estimate ? Margin of Error
Margin of Error = (# of Standard errors)*(Size of Standard Error)
Population proportion p (n large)
?
/2
Population difference p1-p2 (n1, n2 large) Population mean (n30, known)
1
-
2
?
/2
11
+
22
? /2
Brian Powers, Summer 2014
Stat 101 Formulas
Population mean (n ||)
calculator normalcdf(z,10) normalcdf(-10,z) 2*normalcdf(|z|,10)
Brian Powers, Summer 2014
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