Learning Objectives
- Understand the nature of statistics and the statistical investigation cycle.
- Differentiate clearly between a Population and a Sample.
- Classify data into Categorical (Nominal/Ordinal) and Numerical (Discrete/Continuous).
- Formulate valid statistical questions that anticipate variability.
- Understand the purpose of sampling and the concept of bias.
Interactive Study Tools
These tools are here to help students slow down and think about the method before rushing to an answer.
Study Planner
Use this to break a topic into small study sessions.
Method Reminder
This quick guide reminds students what to do when they feel stuck.
- Read the story: what is the question really asking?
- Choose the method: identify the correct idea before calculating.
- Show the reason: do not skip the logic.
- Check the answer: make sure it fits the situation.
1. Formulating Statistical Questions
A statistical investigation starts with a question. A valid statistical question must anticipate variability in the data collected. If there is only one exact answer, it is not a statistical question.
Reason: There is only one answer. No variability.
Reason: You will get many different heights when asking different students. It anticipates variability.
2. Populations vs. Samples
In statistics, it is usually too expensive or time-consuming to ask everyone in a group. Instead, we ask a smaller group to represent the whole.
- Population: The entire group of people or objects that you want to draw a conclusion about.
- Sample: A smaller representative subset selected from the population.
- Census: A survey of the entire population (like the Irish National Census).
Population: All students in the school.
Sample: The 50 randomly selected students.
3. Types of Data
This is guaranteed to appear on your paper! You must be able to classify data into one of four distinct categories.
A. Categorical Data (Words/Categories)
- Nominal: Categories with NO natural order. (e.g., Eye colour, car brands, favourite subject).
- Ordinal: Categories that HAVE a natural order or ranking. (e.g., Exam grades A/B/C, satisfaction ratings Poor/Good/Excellent, T-shirt sizes S/M/L).
B. Numerical Data (Numbers)
- Discrete: Numbers that are counted in exact, distinct values. They cannot take on every possible decimal value. (e.g., Number of siblings, number of cars in a car park).
- Continuous: Numbers that are measured and can take on any value within a range, including infinite decimals. (e.g., Height, weight, time taken to run 100m, temperature).
📝 Exam Style Questions
Easy Q1: State whether the following data is Categorical Nominal, Categorical Ordinal, Numerical Discrete, or Numerical Continuous:
(a) The number of pages in a book.
(b) The flavours of ice cream sold in a shop.
(c) The finishing positions in a marathon (1st, 2nd, 3rd...).
Medium Q2: A researcher wants to find out the average commute time for workers in Galway. They stand outside a train station in Galway at 8:00 AM and survey the first 100 people who walk past.
(a) What is the population?
(b) Give one reason why this sample might be biased.
Hard Q3: "How much pocket money do 1st Year students get per week?" Explain why this is a valid statistical question, and state the type of data that will be collected.
A1:
(a) Numerical Discrete (You count the pages, no half pages).
(b) Categorical Nominal (Words, no natural mathematical order).
(c) Categorical Ordinal (Words/Categories that have a strict ranking/order).
A2:
(a) The population is all workers in Galway.
(b) Bias: They are only surveying people who take the train. They are completely missing people who drive, walk, or cycle, meaning the commute times collected will not accurately represent all workers.
A3: It is a valid statistical question because it anticipates variability (different students will receive different amounts of pocket money). The data collected will be Numerical Continuous (money can take on decimal values like €12.50) OR Numerical Discrete (if restricted to whole euros). *Note: The SEC usually accepts Continuous for money due to cents, but Discrete is accepted if adequately justified.*
🔥 Challenge Questions (No Peeking!)
Easy C1: Change this non-statistical question into a statistical question: "Did John pass his driving test?"
Medium C2: You want to gather data on the colour of cars passing your school. Name the type of data, and suggest a suitable data collection sheet you could use.
Hard (HL) C3: Explain the difference between primary data and secondary data, giving one advantage of each.
(Answers at the very bottom of the page)
📌 Quick Summary
1. Statistical Questions: Must anticipate variability (multiple different answers).
2. Population vs Sample: Population = Everyone. Sample = A small, representative test group.
3. Categorical Data: Words! Nominal = No order (Red, Blue). Ordinal = Order (Small, Medium, Large).
4. Numerical Data: Numbers! Discrete = Counted (number of dogs). Continuous = Measured (weight of dog).
🎓 Final Examiner Advice
Questions on types of data are basically "free marks" if you memorize the four categories. When asked to identify the type of data, ALWAYS provide both words (e.g., don't just say "Numerical", say "Numerical Continuous"). In questions about bias, always think about "Who is being left out?" to easily spot why a sample is unfair.
Challenge Answers:
C1: "What percentage of people in Ireland pass their driving test on the first attempt?" (Anticipates variability in the population).
C2: The data is Categorical Nominal. A suitable collection sheet would be a Tally Chart listing common colours (Red, Black, Silver, White, Other) with space to make tally marks.
C3: Primary data is collected first-hand by the researcher (e.g., conducting a survey yourself). Advantage: You know exactly how it was collected and it perfectly fits your specific question. Secondary data is collected by someone else (e.g., using CSO census data online). Advantage: It is usually much faster, cheaper, and often involves a much larger sample size than you could gather yourself.