Chapter 2 • Organizing and Graphing Data
•Relative frequency of a class = f∕∑f
•Percentage of a class = (Relative frequency) × 100%
•Class midpoint or mark = (Upper limit + Lower limit)∕2
•Class width = Upper boundary − Lower boundary
•Cumulative relative frequency
=Cumulative frequency
Total observations in the data set
• Cumulative percentage
= (Cumulative relative frequency) × 100%
Chapter 3 • Numerical Descriptive Measures
• Mean for ungrouped data: μ=∑x∕N and x=∑x∕n
• Mean for grouped data: μ=∑mf∕N and x=∑mf∕n
where m is the midpoint and f is the frequency of a class
• Weighted Mean for ungrouped data = ∑xw∕∑w
• k% Trimmed Mean = Mean of the values after dropping
k% of the values from each end of
the ranked data
• Median for ungrouped data
= Value of the middle term in a ranked data set
• Range = Largest value − Smallest value
• Variance for ungrouped data:
σ2=
∑x2−((∑x)2
N)
N
and
s2=
∑x2−((∑x)2
n)
n−1
where σ2 is the population variance and s2 is the sample variance
• Standard deviation for ungrouped data:
σ=R∑x2−((∑x)2
N)
N
and
s=R∑x2−((∑x)2
n)
n−1
where σ and s are the population and sample standard devia-
tions, respectively
• Coefficient of variation =σ
μ×100%
or s
x×100%
• Variance for grouped data:
σ2=
∑m2f−((∑mf)2
N)
N
and
s2=
∑m2f−((∑mf)2
n)
n−1
• Standard deviation for grouped data:
σ=R∑m2f−((∑mf)2
N)
N and s=R∑m2f−((∑mf)2
n)
n−1
• Chebyshev’s theorem:
For any number k greater than 1, at least (1 − 1∕k2) of the
values for any distribution lie within k standard deviations
of the mean.
• Empirical rule:
For a specific bell-shaped distribution, about 68% of the
observations fall in the interval (μ − σ) to (μ + σ), about
95% fall in the interval (μ − 2σ) to (μ + 2σ), and about
99.7% fall in the interval (μ − 3σ) to (μ + 3σ).
•Q1 = First quartile given by the value of the middle term
among the (ranked) observations that are less than the
median
Q2 = Second quartile given by the value of the middle term
in a ranked data set
Q3 = Third quartile given by the value of the middle term
among the (ranked) observations that are greater than
the median
• Interquartile range: IQR = Q3 − Q1
• The kth percentile:
Pk=Value of the (k n
100)th term in a ranked data set
• Percentile rank of xi
=Number of values less than xi
Total number of values in the data set ×100
Chapter 4 • Probability
• Classical probability rule for a simple event:
P(Ei)=1
Total number of outcomes
• Classical probability rule for a compound event:
P(A)=Number of outcomes in A
Total number of outcomes
• Relative frequency as an approximation of probability:
P(A)=f
n
• Conditional probability of an event:
P(A∣B)=P(A and B)
P(B)
and
P(B∣A)=P(A and B)
P(A)
• Condition for independence of events:
P(A)=P(A∣B)
and∕or
P(B)=P(B∣A)
• For complementary events: P(A) + P(A) = 1
• Multiplication rule for dependent events:
P(A and B)=P(A) P(B∣A)
• Multiplication rule for independent events:
P(A and B)=P(A) P(B)
FormulaCard.indd Page 1 12/01/16 7:28 AM f-389 FormulaCard.indd Page 1 12/01/16 7:28 AM f-389 /208/WB01777/9781119055716/bmmatter/208/WB01777/9781119055716/bmmatter
Adapted from Prem S. Mann, Introductory Statistics, 9th ed. (Hoboken, NJ: Wiley, 2016)
[VitalSource]. This material is reproduced with the permission of John Wiley & Sons Canada, Ltd.
KEY FORMULAS
Prem S. Mann • Introductory Statistics, Ninth Edition
