Frequently Used Statistics Formulas and Tables
Frequently 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
n = sample size N = population size f = frequency =sum w = weight
Sample mean: x = x n
Population mean: ? = x N
Weighted mean: x = (w ? x) w
Mean for frequency table: x = ( f ? x) f
Midrange = highest value + lowest value 2
Range = Highest value - Lowest value
Sample standard deviation: s = (x - x )2 n -1
Population standard deviation: = (x - ?)2 N
Sample variance: s2
Population variance: 2
Chapter 3
Limits for Unusual Data Below : ? - 2 Above: ? + 2
Empirical Rule About 68%: ?- to ? + About 95%: ?-2 to ? + 2 About 99.7%: ?-3 to ? + 3
Sample coefficient of variation:
CV = s x
100%
Population coefficient of variation:
CV = ?
100%
Sample standard deviation for frequency table: s = n [ ( f ? x2 ) ] -[ ( f ? x) ] 2 n (n -1)
Sample z-score: z = x - x s
Population z-score: z = x - ?
Interquartile Range: (IQR=) Q3 - Q1
Modified Box Plot Outliers lower limit: Q1 - 1.5 (IQR) upper limit: Q3 + 1.5 (IQR)
Chapter 4
Probability of the complement of event A P(not A) = 1 - P( A)
Multiplication rule for independent events P( A an= d B) P( A) ? P(B)
General multiplication rules P( A an= d B) P( A) ? P(B, given A) P( A an= d B) P( A) ? P( A, given B)
Chapter 5 Discrete Probability Distributions:
Mean of a discrete probability distribution: ? =[x ? P(x)] Standard deviation of a probability distribution: = [x2 ? P(x)] - ? 2
Addition rule for mutually exclusive events P( A or B) = P( A) + P(B)
General addition rule = P( A or B) P( A) + P(B) - P( A and B)
Permutation rule:
n Pr
=
n! (n - r)!
Combination rule:
n Cr
=
n! r!(n - r)!
Binomial Distributions
r = number of successes (or x) p = probability of success q = probability of failure q = 1- p p + q = 1
Binomial probability distribution P(r) = nCr pr qn-r
Mean: ? = np
Standard deviation: = npq
Permutation and Combination on TI 83/84
n Math PRB nPr enter r
n Math PRB nCr enter r
Note: textbooks and formula sheets interchange "r" and "x" for number of successes
Poisson Distributions
r = number of successes (or x) ? = mean number of successes
(over a given interval) Poisson probability distribution
P(r) = e-? ?r r!
e 2.71828 ? = mean (over some interval)
= ? 2 =?
2
Chapter 6 Normal Distributions
Raw score: =x z + ? Standard score: z = x - ?
Mean of x distribution: ?x = ?
Standard deviation of x distribtuion:
x
=
n
(standard error)
Standard score for x : z = x - ? / n
Chapter 7
One Sample Confidence Interval
for proportions (p) : (np > 5 and nq > 5)
p^ - E < p < p^ + E
where E = z / 2 p^ = r n
p(1- p) n
for means (?) when is known:
x-E ................
................
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