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ExamsLogic Revision Series | Independent study guide based on the official curriculum.
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Ordinary Level Mathematics Revision Notes

Topic 1.5: Finding, Collecting and Organising Data

These notes explain Finding, Collecting and Organising Data in simple English so students can understand the topic clearly, not just memorise rules. The Ordinary Level version keeps the focus on the core ideas without unnecessary higher-only pressure.

Curriculum Irish Leaving Certificate
Subject Mathematics
Level Ordinary Level
Premium feature Teacher-style explanations and cleaner study flow
Focus
Understanding before memorising
Interactive
Study tools and guided structure
Question Style
Explained examples and exam practice
Format
Website reading and printable notes

Subtopics Covered

  • Primary vs. Secondary Data
  • Simple Random Sampling
  • Bias and Survey Design
  • Observational Studies vs. Designed Experiments
  • 📝 Exam Style Questions
  • 🔥 Challenge Questions (No Peeking!)

What Makes This Version Better

  • Cleaner Ordinary Level focus with no unnecessary higher-only material
  • Simple teacher-style explanations before each method
  • Worked examples in clear stages
  • Cleaner page flow for student understanding
  • SEO-friendly website naming and branding
Disclaimer This publication is an independent educational resource developed by ExamsLogic and compiled by experienced educators. It is based on publicly available official curricula, including Cambridge, Pearson Edexcel, IB, and the Irish Leaving Certificate. This product is not endorsed by, affiliated with, or sponsored by any examination board or governing authority. All registered trademarks remain the property of their respective owners.

Learning Objectives

What You Should Be Able To Do
  • Understand the difference between Primary and Secondary Data.
  • Explain what a Simple Random Sample is and how to generate one.
  • Identify sources of Bias in data collection and survey design.
  • Design fair, unbiased questionnaires.
  • Distinguish between Observational Studies and Designed Experiments.

Interactive Study Tools

These tools are here to help students slow down and think about the method before rushing to an answer.

Tool 1

Study Planner

Use this to break a topic into small study sessions.

Plan: A clear breakdown will appear here.
Tool 2

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. Primary vs. Secondary Data

Simple explanation: This section explains how to read, organise, and interpret data in a clear exam-friendly way.

Before doing any statistics, you must get your data. There are two main categories of data sources:

  • Primary Data: Data collected by the investigator themselves for a specific purpose (e.g., you handing out a survey in your school, or doing an experiment in a lab).
  • Secondary Data: Data that has already been collected by someone else (e.g., looking up the national census results online, reading a newspaper article, or using historical weather records).
Example 1 (Primary): A student standing at the school gate recording the colour of every car that passes.
Advantage: Exact data needed for their specific project. Disadvantage: Takes a lot of time.
Example 2 (Secondary): A student downloading the "Number of cars sold in Ireland 2023" from the Central Statistics Office (CSO) website.
Advantage: Very fast and usually massive sample sizes. Disadvantage: Might not have the exact specific details the student wanted.
Examiner Tip
💡 Examiner Tip: If an exam question asks for an advantage of Secondary Data, the most reliable answers are: "It is cheaper to obtain," "It is much faster to gather," or "The sample size is usually much larger than what a single person could collect."

2. Simple Random Sampling

Simple explanation: This section explains random events in plain language so students can see the logic behind the outcomes.

A sample is only useful if it represents the population accurately. The gold standard is a Simple Random Sample (SRS).

Definition: A sample selected in such a way that every member of the population has an equal chance of being chosen, and every possible sample of that size has an equal chance of being chosen.

Example 1 (The Hat Method): To pick 5 students from a class of 30. Write everyone's name on identical slips of paper, put them in a hat, mix thoroughly, and draw 5 names without looking.
Example 2 (Random Number Generator): Give every student in a school of 800 a number from 1 to 800. Use a computer or calculator to generate 50 random numbers between 1 and 800. Select those students.
Examiner Secret
🕵️ Examiner Secret: If they ask you "How would you select a simple random sample?", you MUST mention a physical or digital mechanism. Don't just say "pick them randomly." Say "Assign them a number and use a random number generator."
Exam Trap
⚠️ Exam Trap: Stratified Sampling vs Random Sampling. If you want 100 students from a school, and you make sure to pick exactly 20 from each Year Group, that is Stratified, not purely Simple Random! (Though Stratified is often better to ensure fairness across groups).

3. Bias and Survey Design

Simple explanation: This section explains the main idea in simple English first, then builds toward the formal method used in exam questions.

Bias occurs when a sample or a survey method systematically over-represents or under-represents a certain group, leading to inaccurate results.

Sources of Bias:

  • Selection Bias: The sample does not reflect the population (e.g., asking only gym members about their exercise habits).
  • Leading Questions: Phrasing a question to push the respondent towards a specific answer.
  • Non-response Bias: When people chosen for the survey refuse to answer, and those who do answer have very different opinions.
Example 1 (Leading Question): "Do you agree that the terrible, unhealthy food in the canteen should be banned?"
Correction: "How would you rate the healthiness of the canteen food?" (Provide options: Very Unhealthy to Very Healthy).
Example 2 (Overlapping Categories): "How old are you? [0-10] [10-20] [20-30]"
Correction: If someone is 20, they don't know which box to tick! It should be [0-10] [11-20] [21-30].
Common Mistake
❌ Common Mistake: Providing survey options that don't cover everyone. E.g., "How many hours do you study? [1-2] [3-4] [5+]". What if someone studies 0 hours? You must include a "0" or "None" option!

4. Observational Studies vs. Designed Experiments

Simple explanation: This section explains the main idea in simple English first, then builds toward the formal method used in exam questions.

How does the researcher interact with the subjects?

  • Observational Study: The researcher simply observes and records data without interfering or trying to change anything. (e.g., Watching a junction to see how many cars run a red light).
  • Designed Experiment: The researcher intentionally applies a "treatment" or changes a variable to see what effect it has. (e.g., Giving half a group a new study pill, and the other half a placebo, to test memory).
Example 1: A doctor asks 100 patients how much coffee they drink, and checks their blood pressure.
This is an Observational Study. The doctor didn't force them to drink the coffee.
Example 2: A doctor splits 100 patients into two groups. She forces Group A to drink 3 coffees a day, and Group B to drink 0 coffees, then checks blood pressure.
This is a Designed Experiment. A treatment was applied!
Examiner Tip
💡 Examiner Tip: Only a Designed Experiment can truly prove "cause and effect". An observational study can only show a "correlation" (a link), because there might be hidden factors (like stress) causing both the coffee drinking and the high blood pressure!

📝 Exam Style Questions

Simple explanation: This section explains the main idea in simple English first, then builds toward the formal method used in exam questions.

Easy Q1: State one advantage and one disadvantage of using a postal questionnaire to collect primary data.

Medium Q2: A student writes the following survey question: "Most intelligent people love Maths. Do you love Maths? [Yes] [No]". Identify two flaws in this question.

Hard Q3: A researcher wants to find the average height of adult men in Ireland. They go to a professional basketball match in Dublin and randomly select 50 men from the crowd to measure. Explain why this sample is biased and how it will affect the results.

A1: Advantage: People can take their time to answer it privately (good for sensitive topics) and it can reach a wide geographical area. Disadvantage: Very low response rate (most people throw them in the bin!).

A2: Flaw 1: It is a Leading Question. By stating "Most intelligent people love Maths", it pressures the respondent to say Yes so they feel intelligent. Flaw 2: There is no "Don't Know", "Sometimes", or "Neutral" option. It forces a strict binary choice.

A3: Bias: Basketball matches tend to attract taller people (players, families of players, fans of the sport). Because they only sampled at a basketball game, they have excluded men who do not attend these games. Effect: The average height calculated will be significantly higher than the true national average. It is an unrepresentative sample.

🔥 Challenge Questions (No Peeking!)

Simple explanation: This section explains the main idea in simple English first, then builds toward the formal method used in exam questions.

Easy C1: Is the data collected in the Irish National Census primary or secondary data to the Irish Government?

Medium C2: You want to design a survey to find out how much money students spend on lunch. Write a well-designed question with appropriate tick-boxes to gather this data.

Hard (HL) C3: Explain the concept of a "Control Group" in a designed experiment.

(Answers at the very bottom of the page)

📌 Quick Summary

1. Primary = You collect it. Secondary = Someone else collected it.
2. Simple Random Sample: Everyone has an equal chance. Use a random number generator.
3. Survey Rules: No leading questions, no overlapping boxes (1-5, 6-10), and always provide a "Zero" or "Other" option.
4. Experiment vs Observation: If you apply a treatment/change things, it's an experiment. If you just watch, it's observational.

🎓 Final Examiner Advice

When critiquing a survey question on the exam, be specific. Don't just say "It's a bad question." Say "The boxes overlap," or "It is a leading question that introduces bias." Knowing the exact terminology will turn a 2-mark attempt into a 5-mark perfect answer. Always imagine yourself filling out the survey: if you wouldn't know what box to tick, there's a flaw in the design!




Challenge Answers:
C1: It is Primary Data to the government (because they collected it themselves for their own purposes). If YOU use it for a school project, it becomes Secondary Data to you.
C2: "How much do you typically spend on lunch per school day?" [€0] [€0.01 - €2.00] [€2.01 - €4.00] [€4.01 - €6.00] [More than €6.00]. (Notice: No overlaps, covers all possibilities including zero).
C3: A Control Group is a group in an experiment that does NOT receive the active treatment (they might receive a fake pill/placebo instead). This provides a baseline to compare the actual treatment against, proving that any changes were actually caused by the treatment and not just natural time or the placebo effect.