Stat 101 Formulas Sample Statistics - University of Illinois ...
Stat 101 Formulas
Sample Statistics
Sample mean
5-Number summary
?0 = ???????
?1 = 1?? ????????
?2 = ??????
?3 = 3?? ????????
?4 = ???????
Range
????? = ??????? ? ???????
= ?4 ? ?0
?
?? =
1
??
?
?=1
Sample variance
?
??2 ? ??? 2
1
2
2
? =
(?? ? ?? ) =
??1
??1
?=1
Sample standard deviation
?
?=
? 2
1
=
(?? ? ?? )2
??1
Inter-Quartile Range
??? = ?3 ? ?1
Fences for Outliers
?1 ? 1.5 ? ???, ?3 + 1.5 ? ???
?=1
Simple Linear Regression
Sample Covariance
Regression Model
?? = ? + ??
Slope
??
?=?
??
Intercept
? = ?? ? ???
Residual
?????? = ?? ? ??? = ?? ? (? + ??? )
?? ?? ? ??? ??
???(?, ?) =
(? ? 1)
Sample Correlation
???(?, ?) ?? ?? ? ??? ??
?=
=
?? ??
(? ? 1)?? ??
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
?
?
? = ?(?) = ?? ? ?(? = ?? ) = ?? ? ??
?=1
?=1
Variance
?
2
? = ???(?) = ?((? ? ?)
2)
= ?(?
2)
2
? ? = (? ? ?)2 ? ??
?=1
Linearity of Expected Value
?(??) = ??(?)
?(? + ?) = ?(?) + ?
?(? + ?) = ?(?) + ?(?)
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)
??1 ??1 ?? 2 ??2
??1 ? ?? 2 ??/2 ?
+
?
?
?
Population mean (n30, known)
?? ??/2 ?
?
Brian Powers, Summer 2014
Stat 101 Formulas
Population mean (n ................
................
In order to avoid copyright disputes, this page is only a partial summary.
To fulfill the demand for quickly locating and searching documents.
It is intelligent file search solution for home and business.
Related searches
- university of illinois online degrees
- university of illinois online degree
- university of illinois at chicago online
- university of illinois chicago online degrees
- university of illinois chicago online
- university of illinois online masters degrees
- university of illinois online programs
- university of illinois urbana champaign online
- university of illinois springfield online
- university of illinois athletics
- university of illinois directory
- university of illinois application