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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