STA 261 EXAM SCRIPT 2025/2026 QUESTIONS WITH
SOLUTIONS RATED A+
✔✔Which Type of Variable?
The length of time to run a 5K - ✔✔continuous quantitative
✔✔Categorical & Quantitative Data
Displays - ✔✔• Frequency and relative frequency tables
• Pie charts
• Bar charts & Pareto charts
• Dotplots
• Stemplots
• Histograms
• Time Series plots
• Boxplots
✔✔How do you know when to use more than one
line per stem on a stem plot? - ✔✔Options for multiple line stemplots: 2, 5, 10
✔✔What is a Deviation? - ✔✔A directed distance from the mean
✔✔Measures of Spread - ✔✔Range = Maximum value - minimum value
• Reported when reporting mean, median, or mode
• IQR = Q3 - Q1
• Reported when reporting median
Standard deviation, 𝑠 =
square root of ((𝑥−u)^2)/𝑛−1
• Reported when reporting mean
✔✔Boxplots - ✔✔Boxplots
• 5-number summary: min, Q1, median, Q3, max
• IQR = Q3 - Q1
• Upper fence = Q3 + 1.5(IQR)
• Lower fence = Q1 - 1.5(IQR)
• Adjacent value = if outliers are present, the
closest value to the fence while remaining
inside the fence
✔✔SOCS from Graphs - ✔✔Shape: mention modality and "skewness"
• Outliers: use fences to help you determine outliers
- Lower Fence = Q1 - 1.5(IQR) Uppper Fence = Q3 + 1.5(IQR)
• Center: report which measure of center that best
describes the "typical" value
- Mean, median, or mode
, • Spread: report the measure of spread that is paired with
your measure of center
- Mean & Standard deviation
- Median & IQR (Range)
- Mode & Range
✔✔Z-scores - ✔✔A measure associated with each observation
that indicates the distance from the
population mean in standard deviations
• Also referred to as a standardized variable
• A measure of relative standing
• Can be used to compare observations from
different populations
𝑧=
𝑥−𝜇
�
✔✔The Empirical Rule - ✔✔Only applies to approx. normal distributions
• Approx. 68% of all obs. w/in 1 std dev of mean
• Approx. 95% of all obs. w/in 2 std dev of mean
• Approx. 99.7% of all obs. w/in 3 std dev of
mean
✔✔Observational Studies - ✔✔Researchers observe characteristics and take
measurements
- Observational studies can only reveal association or correlation
retrospective, prospective or sample survey
✔✔Retrospective study - ✔✔conducting an analysis on the past
- Identify subjects with a specific characteristic and then look into
their history to find things that may be related
- Prone to errors
- Example: Case-control study
✔✔Prospective study - ✔✔identifying subjects in advance and
then collecting data as events unfold
- Example: Cohort study
✔✔Sample survey - - ✔✔takes cross section of a population at a
given time
- Also called a cross-sectional study
✔✔Experimental Studies - ✔✔Designed experiments - researchers impose treatments
and controls
SOLUTIONS RATED A+
✔✔Which Type of Variable?
The length of time to run a 5K - ✔✔continuous quantitative
✔✔Categorical & Quantitative Data
Displays - ✔✔• Frequency and relative frequency tables
• Pie charts
• Bar charts & Pareto charts
• Dotplots
• Stemplots
• Histograms
• Time Series plots
• Boxplots
✔✔How do you know when to use more than one
line per stem on a stem plot? - ✔✔Options for multiple line stemplots: 2, 5, 10
✔✔What is a Deviation? - ✔✔A directed distance from the mean
✔✔Measures of Spread - ✔✔Range = Maximum value - minimum value
• Reported when reporting mean, median, or mode
• IQR = Q3 - Q1
• Reported when reporting median
Standard deviation, 𝑠 =
square root of ((𝑥−u)^2)/𝑛−1
• Reported when reporting mean
✔✔Boxplots - ✔✔Boxplots
• 5-number summary: min, Q1, median, Q3, max
• IQR = Q3 - Q1
• Upper fence = Q3 + 1.5(IQR)
• Lower fence = Q1 - 1.5(IQR)
• Adjacent value = if outliers are present, the
closest value to the fence while remaining
inside the fence
✔✔SOCS from Graphs - ✔✔Shape: mention modality and "skewness"
• Outliers: use fences to help you determine outliers
- Lower Fence = Q1 - 1.5(IQR) Uppper Fence = Q3 + 1.5(IQR)
• Center: report which measure of center that best
describes the "typical" value
- Mean, median, or mode
, • Spread: report the measure of spread that is paired with
your measure of center
- Mean & Standard deviation
- Median & IQR (Range)
- Mode & Range
✔✔Z-scores - ✔✔A measure associated with each observation
that indicates the distance from the
population mean in standard deviations
• Also referred to as a standardized variable
• A measure of relative standing
• Can be used to compare observations from
different populations
𝑧=
𝑥−𝜇
�
✔✔The Empirical Rule - ✔✔Only applies to approx. normal distributions
• Approx. 68% of all obs. w/in 1 std dev of mean
• Approx. 95% of all obs. w/in 2 std dev of mean
• Approx. 99.7% of all obs. w/in 3 std dev of
mean
✔✔Observational Studies - ✔✔Researchers observe characteristics and take
measurements
- Observational studies can only reveal association or correlation
retrospective, prospective or sample survey
✔✔Retrospective study - ✔✔conducting an analysis on the past
- Identify subjects with a specific characteristic and then look into
their history to find things that may be related
- Prone to errors
- Example: Case-control study
✔✔Prospective study - ✔✔identifying subjects in advance and
then collecting data as events unfold
- Example: Cohort study
✔✔Sample survey - - ✔✔takes cross section of a population at a
given time
- Also called a cross-sectional study
✔✔Experimental Studies - ✔✔Designed experiments - researchers impose treatments
and controls
