Frequently Used Statistics Formulas and Tables
嚜澹requently Used Statistics Formulas and Tables
Chapter 2
Class Width =
highest value - lowest value
(increase to next integer)
number classes
Class Midpoint =
upper limit + lower limit
2
Chapter 3
Chapter 3
n = sample size
N = population size
f = frequency
曳 =sum
w = weight
Limits for Unusual Data
Below : ? - 2考
Above: ? + 2考
Empirical Rule
About 68%: ? -考 to ? + 考
About 95%: ? -2考 to ? + 2考
About 99.7%: ? -3考 to ? + 3考
﹉x
n
﹉x
Population mean: ? =
N
﹉( w ? x)
Weighted mean: x =
﹉w
Sample mean: x =
Sample coefficient of variation: CV =
s
? 100%
x
Population coefficient of variation: CV =
﹉( f ? x)
﹉f
highest value + lowest value
Midrange =
2
Mean for frequency table: x =
Sample standard deviation for frequency table:
s=
n [ ﹉( f ? x 2 ) ] ? [ ﹉( f ? x) ]
n (n ? 1)
Range = Highest value - Lowest value
Sample standard deviation: s =
﹉( x ? x )
n ?1
Population standard deviation: 考 =
Sample z-score: z =
2
﹉( x ? ? )
N
2
x?x
s
Population z-score: z =
x??
考
Interquartile Range: (IQR)
= Q3 ? Q1
Sample variance: s 2
Population variance: 考 2
考
? 100%
?
Modified Box Plot Outliers
lower limit: Q1 - 1.5 (IQR)
upper limit: Q3 + 1.5 (IQR)
2
Chapter 4
Chapter 5
Probability of the complement of event A
P (not A) = 1 - P ( A)
Discrete Probability Distributions:
Mean of a discrete probability distribution:
? =﹉[ x ? P( x)]
Multiplication rule for independent events
P ( A and
=
B)
P ( A) ? P ( B )
Standard deviation of a probability distribution:
General multiplication rules
P ( A and
=
B)
P ( A) ? P ( B, given A)
P ( A and
=
B)
P ( A) ? P ( A, given B )
考 = ﹉[ x 2 ? P( x)] ? ? 2
Addition rule for mutually exclusive events
P ( A or B ) = P ( A) + P ( B )
Binomial Distributions
General addition rule
=
P ( A or B )
P ( A) + P ( B ) ? P ( A and B )
q = probability of failure
q=
1? p
p + q=1
r = number of successes (or x)
p = probability of success
Binomial probability distribution
P ( r ) = n Cr p r q n ? r
n!
Permutation rule: n Pr =
(n ? r )!
Combination rule:
n Cr
=
Mean: ? = np
n!
r !(n ? r )!
Standard deviation: 考 = npq
Poisson Distributions
Permutation and Combination on TI 83/84
n
Math
PRB
nPr
enter
r = number of successes (or x)
? = mean number of successes
r
(over a given interval)
Poisson probability distribution
n
Math
PRB
nCr
enter
r
e? ? ? r
P(r ) =
r!
e > 2.71828
Note: textbooks and formula
sheets interchange ※r§ and ※x§
for number of successes
? = mean (over some interval)
考= ?
考2 = ?
2
Chapter 6
Chapter 7
Confidence Interval: Point estimate ㊣ error
Normal Distributions
Raw score: =
x z考 + ?
Standard score: z =
Point estimate = Upper limit + Lower limit
2
x??
考
Error = Upper limit - Lower limit
2
Mean of x distribution: ? x = ?
Sample Size for Estimating
Standard deviation of x distribtuion: 考 x =
(standard error)
Standard score for x : z =
考
n
means:
?z 考 ?
n = ? 汐 /2 ?
? E ?
x ??
2
proportions:
考/ n
2
?z
?
? ? ? 汐 / 2 ? with preliminary estimate for p
n = pq
? E ?
Chapter 7
2
?z
?
n = 0.25 ? 汐 / 2 ? without preliminary estimate for p
? E ?
One Sample Confidence Interval
(np > 5 and nq > 5)
for proportions (p) :
variance or standard deviation:
*see table 7-2 (last page of formula sheet)
p? ? E < p < p? + E
where E = z汐 / 2
p? =
p(1 ? p)
n
Confidence Intervals
Level of Confidence
r
n
for means (? ) when 考 is known:
x?E ................
................
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