Stat 101 Formulas Sample Statistics .edu

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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