12 / 68
Descriptive Statistics for Ungrouped Data
•
Mean:
¯
x
=
n
i
=1
x
i
n
,
where
n
is sample size
µ
=
N
i
=1
x
i
N
,
where
N
is population size
•
Population variance:
σ
2
=
N
i
=1
(
x
i
−
µ
)
2
N
•
Sample variance:
s
2
=
n
i
=1
(
x
i
−
¯
x
)
2
n
−
1
Chebyshev’s Theorem
•
At least
(1
−
1
k
2
)
data fall within
(
µ
±
kσ
)
or
At least
(1
−
1
k
2
)
data fall within
(¯
x
±
ks
)
Rules of Probability
•
Addition Rule:
P
(
A
∪
B
) =
P
(
A
) +
P
(
B
)
−
P
(
A
∩
B
)
•
Subtraction Rule:
P
(
A
) = 1
−
P
(
A
)
•
Multiplication Rule:
P
(
A
∩
B
) =
P
(
B
)
·
P
(
A
|
B
)
Theory of Probability
•
Independence Event:
P
(
A
∩
B
) =
P
(
A
)
·
P
(
B
)
•
Conditional Event:
P
(
A
|
B
) =
P
(
A
∩
B
)
P
(
B
)
Bayes’ Theorem
•
P
(
B
k
|
A
) =
P
(
B
k
)
P
(
A
|
B
k
)
n
i
=1
P
(
B
i
)
P
(
A
|
B
i
)
2
Statistical Tables and Formulae 2.0