Published on 5 Oct 2020

School

Department

Course

Professor

1

Formula Sheet [SS 2J03]

Mean for population data:

N

x

=

Mean for sample data:

n

x

x

=

Variance and Standard Deviation for

Ungrouped Data

( )

( )

( )

( )

1

and

1

and

2

2

2

2

2

2

−

−

=

−

=

−

−

=

−

=

n

xx

s

N

x

n

xx

s

N

x

Short-cut version:

( ) ( )

( ) ( )

1

and

1

and

2

2

2

2

2

2

2

2

2

2

−

−

=

−

=

−

−

=

−

=

n

n

x

x

s

N

N

x

x

n

n

x

x

s

N

N

x

x

Coefficient of Variation (CV):

%100 CV :data sampleFor

%100 CV :data populationFor

=

=

x

s

Mean for Grouped Data:

N

mf

=

n

mf

x

=

Variance and Standard Deviation for Grouped

Data:

( )

( )

1

and

2

2

2

2

−

−

=

−

=

n

xmf

s

N

mf

Short-Cut version:

( )

1

and

)( 2

2

2

2

2

2

−

−

=

−

=

n

n

mf

fm

s

N

N

mf

fm

Chebyshev’s Theorem:

For any number k greater than 1, at least

(1 – 1/k²) of the data values lie within k

standard deviations of the mean.

Empirical Rule:

For a bell-shaped distribution, approximately

68% of the observations lie within one

standard deviation of the mean

95% of the observations lie within two

standard deviations of the mean

99.7% of the observations lie within

three standard deviations of the mean

Addition Rule to Find the Probability of the

Union of Mutually Exclusive Events

P (A or B) = P(A) + P(B)

Addition Rule to Find the Probability of Union

of Two Mutually Nonexclusive Events

P (A or B) = P(A) + P(B) – P(A and B)

Joint Probability of Two Dependent Events:

P (A and B) = P(A) x P(B |A) or P(B) x

P(A |B)

Joint Probability of Independent Events:

P (A and B) = P(A) x P(B)