Statistics 9 – Cycle 2 Study Notes

Course: Statistics 9
- Instructor: Teacher Fred
- Cycle 2 Dates: June 18 – 25, 2025
School-culture reminders
- “Prayer changes things.”
- “Attendance matters – all day, every day.”
- “Spray Time – Stay Safe” (health/sanitation protocol)

Simulation goal: form groups quickly under different categorical rules; points awarded for correct grouping.
Guidelines
• The teacher flashes a characteristic + required group size.
• Everyone may attempt each round; 1 pt per member of every correct group; non-grouped students earn 0 pts.
Prompt sequence & implicit statistical ideas
1. “Group into FOUR – unspecified variable (open-ended).
2. “Group into TWO by Birth Month.” → Highlights a qualitative, nominal variable with 12 categories.
3. “Group into THREE by Gender.” → Categorical; modern discussion can address inclusivity beyond male/female.
4. “Group into TWO by Zodiac Sign.” → Dichotomizing a naturally 12-category variable; shows how researchers sometimes collapse categories.
5. “Group into FIVE by Hometown.” → Demonstrates large, possibly non-exhaustive set of categories.
Pedagogical purpose
• Sets the tone for qualitative vs. quantitative variables, grouping, and sampling.
• Reveals natural variation and the difficulty of fitting into rigid sample frameworks.

Population vs. Sample: Differentiate through hands-on brainstorming.
Variables: Correctly identify dependent (DV) and independent (IV) variables in real or hypothetical studies.
Measurement Levels: Classify variables as Nominal, Ordinal, Interval, Ratio and illustrate each with daily-life examples.

Logistics
• Class split into groups of 5; colored pens supplied.
• Stations posted on walls; groups rotate (“carousel”) until all prompts answered.
Guiding questions
1. Difference between a population and a sample?
2. Everyday scenarios demonstrating population vs. sample.
3. How to distinguish a dependent from an independent variable?
4. Identify the four measurement levels and give daily illustrations.
Visual Easter-eggs on the slide
• Scribbles: $456$ , $78$ , $+0\times1$ , $10{:}00$ , $V=\pi r h$ , $y = m x + b$ — hints at quantitative variables (time, arithmetic, geometry, linear equations).

DEFINITIONS
• Population: Entire group from which we hope to draw conclusions.
• Sample: Subset actually observed/measured; always smaller than population.
Examples supplied
• Populations:
– All learners of PYCS.
– All PYCS faculty & staff.
– Every country in the world.
• Samples:
– Grade 9 students of PYCS.
– All DCs among office employees.
– Asian countries worldwide.
Quick-fire Classification (slides 23–26)
1. “100 randomly selected students” → Sample.
2. “Every registered car in a country” → Population.
3. “Subset of 1000 social-media users analyzed for overall behavior” → Sample.
4. “Survey of 500 randomly chosen city residents” → Sample.
Significance
• Good sampling yields generalizable inference; bad sampling → bias.
• Recognizing when you have the whole population vs. a sample affects which statistical formulas (e.g., $\sigma$ vs. $s$ ) you use.

Independent Variable (IV)
• Synonyms: predictor, explanatory, manipulated factor.
• Researcher controls or classifies it.
• Hypothesized cause or influence.
Dependent Variable (DV)
• Synonyms: outcome, response variable.
• Measured/observed for change.
• Hypothesized effect, depends on IV.
Common mnemonic: “I change – D measures.”
Reflective question (slide 46):
• “How can knowing about IVs make you more independent/responsible?”
– Mapping personal choices (IVs) to life outcomes (DVs) encourages ownership of decisions.

Nominal
• Pure labels; categories are mutually exclusive & exhaustive; no inherent order.
• Examples: city of birth, gender, ethnicity, marital status, car brand.
Ordinal
• Ordered categories; relative ranking; intervals unknown/unequal.
• Examples: Mobile Legends rank, letter grades, cancer stages, satisfaction scales, Olympic medal tally (top 5), burn degree, frequency/Likert items.
Interval
• Ordered, equal intervals, no true zero (zero is arbitrary).
• Permits addition & subtraction; ratios meaningless.
• Examples: shoe size, IQ scores, $^\circ\text{C}$ / $^\circ\text{F}$ temperature, credit score, clock time of day, pH.
Ratio
• Ordered, equal intervals and a true zero → ratios meaningful.
• Examples: weight, height, income, distance, market share, elapsed time, absolute temperature (Kelvin), crime rate.

Summary table cue (slide 39):
• Nominal → categorize.
• Ordinal → rank.
• Interval → equal gaps.
• Ratio → true zero.

Ethical sampling: ensure representativeness, avoid discrimination (e.g., gender categorization beyond binary).
Mislabeling IV/DV may invert causality; responsible analysis demands clarity.
Measurement level dictates permissible statistics:
• Nominal → mode, chi-square.
• Ordinal → median, rank tests.
• Interval/Ratio → mean, SD, parametric tests.
Data stewardship: Privacy of populations/samples, informed consent during surveys.

Previous mathematics content hinted (linear functions $y=mx+b$ , geometry $V=\pi r h$ ) ties into quantitative variables measured at ratio/interval levels.
Builds on scientific-method steps: formulate questions → identify variables → sample → measure → analyze.

Volume of cylinder: $V = \pi r^2 h$ (slide abbreviates radius by (r), height by (h)).
Slope-intercept: $y = m x + b$ .
Null vs. alternative hypotheses rely on population parameters (e.g., $\mu$ , $\sigma$ ) vs. sample statistics (e.g., $\bar{x}$ , $s$ ).

Post-lesson assessment aligns to the three learning targets.
Students likely complete a quiz or reflective worksheet covering:
1. Identify population vs. sample in new scenarios.
2. Label IVs & DVs in brief research vignettes.
3. Classify variables’ measurement levels and justify.
Credits: Template by Slidesgo, icons by Flaticon, images by Freepik.

Create flashcards for IV/DV definitions & examples.
Practice reclassifying variables at different measurement levels when conditions change (e.g., Celsius → interval, Kelvin → ratio).
When reading any study, explicitly ask:
• “What is the population?”
• “What sample was drawn?”
• “What are the IVs & DVs?”
• “At which measurement level is each variable recorded?”