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Number of observations in sample. 3.1. N. Number of observations in population. 3.1 x x-‐bar x = xi ! n. Sample mean. 3.1 μ mu. Population mean.
Typology: Study notes
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Section Symbol Name Formula (if relevant) Description
3.1 n Number of observations in sample
Number of observations in population
x
x-‐bar
x =
x
i
n
Sample mean
μ
mu Population mean
3.1 M Median M =
n + 1
2
th
smallest observation
“Middle” observation
mode
Most frequent observation
Min
Minimum
Min = Smallest Observation Smallest observation
3.2 Max Maximum
Max = Largest Observation
Largest observation
Range R = Max! Min
s
2
s
2
x
i
! x
2
n! 1
Sample variance
s or s
x s = s
2
Sample standard deviation
2
sigma squared Population variance
! or!
x
sigma Population standard deviation
x value! mean
standard deviation
Z-‐score for a given x value
1
1
25
100
th
smallest observation First quartile
3
3
75
100
n + 1
th
smallest observation Third quartile
3
1
Inter quartile range
3.4 UF Upper Fence
3
Upper limit for outliers
Lower Fence
1
Lower limit for outliers
4.1 r Correlation coefficient
a
Slope of linear regression model
4.2 b Intercept of linear regression model
y y-‐hat
y = ax + b Predicted response value
residual
residual = y!
y
Observed y – Expected y
r
2
Coefficient of determination
5.1 E Event space
Sample space
Number of observations in the set X
Probability of event E
!
Z sub alpha
Z-‐score that has! area to the right of it
μ
x
Mu sub x-‐bar
μ
x
= μ
Population mean of sampling distribution
!
x
Sigma sub x-‐bar
!
x
!
n
Population standard deviation of sampling distribution
p
Proportion of population with given attribute
8.2 x Number of sample with given attribute
p p-‐hat
p =
x
n
Proportion of sample with given attribute
μ
p ˆ
mu sub p-‐hat
μ
ˆ p
= p
Population mean of sample proportion
ˆ p Sigma sub p-‐hat !
ˆ p
p ( 1 " p )
n
Population standard deviation of sample proportion
! / 2
T sub alpha/2 T-‐score the has! / 2 area to the right of it
df df = n! 1
Degrees of freedom
0
H naught Null hypothesis
1
H one Alternative hypothesis
μ
0
mu naught Population proportion assuming H
0
is true
p p! value Probability of a result as extreme if H
0
is true
T T! score
x value! mean
sample standard deviation
T-‐ Score for a given x value
p
0
p naught Population proportion assuming H
0
is true
d
d bar
Sample mean of difference
s
d
s sub d Sample standard deviation of difference (dependent)
μ
d
mu sub d Population mean of difference
s
d
s sub d s
d
s
1
2
n
1
s
2
2
n
2
Sample standard deviation of difference (independent)
p
p =
x
1
2
n
1
2
Pooled sample proportion
p ˆ
1
" p ˆ
2
ˆ p 1
"
ˆ p 2
p 1 "
n
1
n
2
Population Standard Deviation of proportion difference
(assuming H
0
is true)
ˆ p 1
"
ˆ p 2
ˆ p
1
" ˆ p
2
p
1
1 " p
1
( )
n
1
p
2
1 " p
2
( )
n
2
Population Standard Deviation of proportion difference
(for confidence intervals)