Statistics – 1st Semester Exam Study Guide
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
The exam will cover material from chapter 1 through chapter 4 in our textbook.
The exam will consist of multiple choice, short answer, and completion questions.
The following definitions, key words, concepts are what we have covered so far.
Please study!
Chapter 1 – The Nature of Probability & Statistics
Cluster sample
Inferential statistics
Continuous variables
Measurement scales (nominal, ordinal, interval,
ratio)
Control group
Data
Data set
Dependent variable
Descriptive statistics
Discrete variables
Independent variable
Population
Probability
Qualitative & quantitative variables
Random sampling
Sample
Stratified sampling
Systematic sampling
Chapter 2 – Frequency Distributions and Graphs
Bar graph
Class
Class boundaries
Class midpoint
Class width
Frequency distribution (categorical, cumulative,
grouped)
Pie graph
Raw data
Stem and leaf plot
Lower & upper class limit
Chapter 2 – Formulas
Formula for range:
R = highest value – lowest value
Formula for class width:
Class width = upper boundary – lower boundary
Formula for class midpoint:
Xm =
𝒍𝒐𝒘𝒆𝒓 𝒍𝒊𝒎𝒊𝒕+𝒖𝒑𝒑𝒆𝒓 𝒍𝒊𝒎𝒊𝒕
𝟐
Chapter 3 – Data Description
Boxplot
Mode
Chebyshev’s theorem
Outlier
Coefficient of variation
Percentile
Data array
Quartile
Five-number summary
Range
Interquartile range (IQR)
Standard deviation
Mean
Variance
Median
z score
Chapter 3 Formulas
Formula for the mean for individual data:
Formula for the variance of sample data:
𝜇=
2
𝑠 =
Formula for the standard deviation for sample data:
2
𝑛(∑ 𝑋 )−(∑ 𝑋)
𝑠=√
𝑛(𝑛−1)
2
∑𝑋
𝑁
𝑛(∑ 𝑋 2 )−(∑ 𝑋)2
𝑛(𝑛−1)
Chapter 4 – Probability and Counting Rules
Combination
Independent events
Complement of an event
Mutually exclusive events
Conditional probability
Outcome
Dependent events
Permutation
Event
Sample space
Fundamental counting rule
Chapter 4 Formulas
Formula for classical probability:
𝑃(𝐸 ) =
𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑜𝑢𝑡𝑐𝑜𝑚𝑒𝑠 𝑖𝑛 𝐸
𝑛(𝐸)
=
𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑜𝑢𝑡𝑐𝑜𝑚𝑒𝑠 𝑖𝑛 𝑠𝑎𝑚𝑝𝑙𝑒 𝑠𝑝𝑎𝑐𝑒 𝑛(𝑆)
Addition rule (mutually exclusive events):
𝑃(𝐴 𝑜𝑟 𝐵) = 𝑃(𝐴) + 𝑃(𝐵)
Addition rule (events are NOT mutually exclusive):
𝑃(𝐴 𝑜𝑟 𝐵) = 𝑃(𝐴) + 𝑃(𝐵) − 𝑃(𝐴 𝑎𝑛𝑑 𝐵)
Multiplication rule (independent events):
𝑃(𝐴 𝑎𝑛𝑑 𝐵) = 𝑃(𝐴) ∗ 𝑃(𝐵)
Multiplication rule (dependent events):
𝑃(𝐴 𝑎𝑛𝑑 𝐵) = 𝑃(𝐴) ∗ 𝑃(𝐵|𝐴)
Formula for conditional probability:
𝑃(𝐵|𝐴) =
𝑃(𝐴 𝑎𝑛𝑑 𝐵)
𝑃(𝐴)
Complementary events:
𝑃(𝐸 ) + 𝑃(𝐸 ′ ) = 1
Formula for Permutation of N objects taken R at a time:
𝑁𝑃𝑅
=(
𝑁!
𝑁−𝑅 )!
Formula for Combination of N objects taken R at a time:
𝑁𝐶𝑅
=
𝑁!
𝑅! (𝑁−𝑅 )!