Download MATH 131 TEST 1: Formulas

ECON 230
Formulas for Test 1
Formula for Mean
For raw data:
x 
For data with
frequencies:
f = frequency
x
x
n
For data grouped
into classes:
m = midpoint
 x  f 
x
n
(where n   f
 m f 
n
)
Formula for Standard Deviation
For raw data:
s
( x  x )
 ( x  )

N
2
n 1
For data with frequencies:
For data grouped into classes:
2
(x  x) f
s
n 1
2
 (m  x ) f
s
n 1
Short-cut formula for standard deviation:
s 
2
x
2
 x

n 1
2
2
n
1
Chebyshev’s Theorem:
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At least 1-1/ k of the data must lie within k standard deviations of the mean.
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For example, if k=3, 1-1/ k =0.89. So 89% of the data must lie within three
standard deviations of the mean.
Empirical Rule:
For normally distributed variables,
68% of the data is within 1 standard deviations of the mean
95% of the data is within 2 standard deviations of the mean
99% of the data is within 3 standard deviations of the mean
Probability:
Multiplication Rule
If events A and B are independent, then
P  A and B   P  A  P  B 
If events A and B are dependent, then
 
P  A and B   P  A  P BA  P( B)  P( AB)
Addition Rule
If events A and B are mutually exclusive, then
P  A or B   P  A  P  B 
If events A and B are not mutually exclusive, then
P  A or B   P  A  P  B   P( A and B)
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