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Math 243 Symbols.pdf, Study notes of Mathematics

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.

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2021/2022

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Section(
Symbol(
Name(
Formula((if(relevant)(
Description(
3.1$
n
$
$
$
Number$of$observations$in$sample$
3.1$
N
$
$
$
Number$of$observations$in$population$
3.1$
x
$
x6bar$
$
Sample$mean$
3.1$
µ
$
mu$
$
Population$mean$
3.1$
M$
Median$
M=n+1
2
( )
th
$$smallest$observation$
Middle”$observation$
3.1$
mode
$$
$
$
Most$frequent$observation$
3.2$
Min
$
Minimum$
Min =Smallest Observation
$
Smallest$observation$
3.2$
Max
$
Maximum$
Max =Largest Observation
$
Largest$observation$
3.2$
R
$
Range$
R=Max !Min
$
$
3.2$
s2
$
$
s2=
xi!x
( )
"2
n!1
$
Sample$variance$
3.2$
sor sx
$
$
s=s2
$
Sample$standard$deviation$
3.2$
!
2
$
sigma$squared$
$
Population$variance$
3.2$
!
or
!
x
$
sigma$
$
Population$standard$deviation$
3.4$
Z
$
$
Z=x value !mean
standarddeviation
$
Z6score$for$a$given$x$value$
3.4$
Q1
$
$
Q1=25
100 n+1
( )
( )
th
$smallest$observation$
First$quartile$
3.4$
Q3
$
$
Q3=75
100 n+1
( )
( )
th
$smallest$observation$
Third$quartile$
3.4$
IQR
$
$
IQR =Q3!Q1
$
Inter$quartile$range$
3.4$
UF
$
Upper$Fence$
UF =Q3+1.5 IQR
( )
$
Upper$limit$for$outliers$
3.4$
LF
$
Lower$Fence$
LF =Q1!1.5 IQR
( )
$
Lower$limit$for$outliers$
4.1$
r
$
$
$
Correlation$coefficient$
4.2$
a
$
$
$
Slope$of$linear$regression$model$
4.2$
b
$
$
$
Intercept$of$linear$regression$model$
4.2$
ˆ
y
$
y6hat$
ˆ
y=ax +b
$
Predicted$response$value$
4.2$
residual
$$
$
residual =y!ˆ
y
$$
Observed$y$–$Expected$y$
4.3$
r2
$$
$
$
Coefficient$of$determination$
5.1$
E
$$
$
$
Event$space$
5.1$
S
$$
$
$
Sample$space$
5.1$
N(X)
$$
$
$
Number$of$observations$in$the$set$X$
5.1$
P(E)
$$
$
$
Probability$of$event$E$
pf2

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Section Symbol Name Formula (if relevant) Description

3.1 n Number of observations in sample

N

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

R

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

3.4 Z

Z =

x value! mean

standard deviation

Z-­‐score for a given x value

Q

1

Q

1

25

100

( n + 1 )

th

smallest observation First quartile

Q

3

Q

3

75

100

n + 1

th

smallest observation Third quartile

IQR

IQR = Q

3

! Q

1

Inter quartile range

3.4 UF Upper Fence

UF = Q

3

+ 1.5 IQR

Upper limit for outliers

LF

Lower Fence

LF = Q

1

! 1.5 ( IQR )

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

S

Sample space

N ( X )

Number of observations in the set X

P ( E )

Probability of event E

Z

!

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

T

! / 2

T sub alpha/2 T-­‐score the has! / 2 area to the right of it

df df = n! 1

Degrees of freedom

H

0

H naught Null hypothesis

H

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

T =

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

  • x

2

n

1

  • n

2

Pooled sample proportion

p ˆ

1

" p ˆ

2

ˆ p 1

"

ˆ p 2

p 1 "

( p )

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)