Collecting Data to Answer Questions (Grade 11 NSC Matric Mathematical Literacy): Revision Notes
Collecting Data to Answer Questions
Introduction
Data collection is the foundation of statistics and helps us answer important questions about the world around us. Before collecting any data, we need to understand what we're looking for and how to gather reliable information that truly represents what we want to study.
Posing questions
The first step in any statistical investigation is asking the right questions. These questions serve multiple important purposes:
- Guide what data to collect - Your questions determine exactly what information you need
- Influence how data is collected - Different questions require different collection methods
- Shape how data is organised - Questions affect how you structure and categorise your data
- Determine appropriate analysis methods - Your questions guide which graphs and calculations to use
Example: Teacher analysing class performance
A teacher wants to understand student performance and might ask:
- How did the class perform overall?
- Did female students perform better than male students?
- Did this class perform better than other classes in the same grade?
These questions will determine how the teacher collects, organises, and analyses the student marks.
The Power of Good Questions
Well-formulated questions are the backbone of any statistical investigation. They not only guide your data collection process but also ensure that the information you gather will actually help answer what you want to know. Poor questions lead to irrelevant data and wasted effort.
Example: Reducing electricity consumption
A homeowner wanting to reduce electricity costs might ask:
- How many units of electricity do I use per month on average?
- How much do I pay for electricity monthly?
- Which appliances use the most electricity?
- Which appliances can I use less often to reduce costs?
Understanding populations and samples
When collecting data, you must clearly distinguish between the population and the sample.
Key Definitions
Population: The entire group about which you want to collect data. This includes everyone or everything you're interested in studying.
Sample: A smaller subset chosen from the population to represent the whole group. We study the sample to make conclusions about the entire population.
Survey: The process of collecting data from a sample or population.
Why use samples?
We often use samples instead of studying entire populations for several practical reasons:
- Practical reasons: Populations are often too large to study completely
- Cost considerations: Studying entire populations can be expensive
- Time constraints: Sampling saves significant time
- Accessibility: Sometimes the entire population is impossible to reach
Example: School transport study
Population = All students in the school
Sample = Selected students from different grades, both male and female, who can be interviewed about their transport methods
This approach allows researchers to understand transportation patterns across the entire school without interviewing every single student.
Example: Health study on malaria
Population = All people in South Africa
Sample = Representative group including males and females from different provinces and racial backgrounds
Studying a carefully chosen sample of thousands is more feasible than attempting to survey all 60+ million South Africans.
Avoiding bias in data collection
Bias occurs when your sample doesn't accurately represent the population, leading to incorrect conclusions.
Requirements for Unbiased Samples
A good sample must be:
- Representative - It must reflect the same characteristics as the population
- Large enough - Small samples may not provide reliable information about the population
- Diverse - It should include different groups within the population
If any of these requirements are not met, your sample will be biased and your conclusions unreliable.
Consequences of bias
If a sample is biased, it provides a skewed or distorted impression of the population's true characteristics. This can lead to wrong decisions and false conclusions about the entire group you're studying.
Example: Studying alcohol abuse at school
Population: All learners in the school
A representative sample must include:
- Both male and female students
- Students from every grade
- Students from all racial backgrounds in correct proportions
- Adequate sample size (e.g., 150-200 students from a school of 980)
Why this matters: If you only interview students from one grade or primarily one gender, your conclusions won't apply to the whole school and will be biased.
Data collection instruments
Once you know what questions to ask and who to study, you need the right tools to gather information effectively.
Types of Data Collection Tools
Questionnaire: A structured document containing questions that people complete themselves or through interviews. Used to gather opinions, personal information, or experiences.
Recording sheet: A document used by researchers to track events, behaviours, or occurrences over time. Usually completed by the person conducting the research.
Example: Medical clinic questionnaire
This questionnaire collects multiple categories of patient information including:
- Personal details (name, age, gender)
- Physical characteristics (height, weight)
- Location (urban/rural residence)
- Medical information (reason for visit, treatment)
The variety of categories allows for comparisons between different patient groups and helps medical staff identify patterns in patient demographics and health issues.
Example: Post office visitor tracking
This recording sheet tracks visitor patterns throughout the week by:
- Recording visitors in 30-minute time intervals
- Tracking daily patterns from Monday to Saturday
- Using checkmarks to count visitor frequency
- Identifying peak and quiet periods
The data helps management make informed decisions about:
- Staff scheduling during busy periods
- Break times for employees
- Resource allocation throughout the day
Worked examples
Worked Example: Car popularity study
Students investigate popular car makes by counting vehicles in a shopping centre car park.
Data collected:
| Make of car | Number of cars |
|---|---|
| Ford | 38 |
| Mazda | 59 |
| BMW | 25 |
| Toyota | 66 |
| Mercedes | 8 |
| Peugeot | 1 |
| Hyundai | 7 |
| Nissan | 52 |
Population: All cars in the town
Sample: Cars parked at one shopping centre
Conclusion: Toyota is most popular (66 cars)
Potential bias: This sample only represents people who shop at this particular centre. Different shopping centres might have different car demographics.
Worked Example: Neighbourhood tearoom feasibility
Martin surveys 60 households about opening a tearoom.
Survey results:
- Total neighbourhood population: ≈ 500 people
- Children/teenagers surveyed: 18
- Women surveyed: 56
- Men surveyed: 53
- Total surveyed: 127 people
Analysis: Martin surveyed of the neighbourhood population. This represents a good sample size with diverse age groups and genders.
Worked Example: School smoking survey
A student conducts a smoking survey to verify newspaper statistics.
Sample composition:
- 200 high school students total
- 100 males, 100 females (50/50 gender split)
- 50 each of Black, Coloured, Asian, and White students (equal racial representation)
Results:
- 26 students smoke (13%)
- 174 students don't smoke (87%)
Conclusion: Only 13% smoke regularly, contradicting higher newspaper statistics.
Why this sample is good: Equal representation of genders and racial groups, large sample size (200 students), and structured methodology.
Common exam tips
When approaching data collection questions in exams, remember these key strategies:
- Always identify the population first - This is the complete group you want to understand
- Check for bias - Ask if the sample truly represents the population
- Consider sample size - Larger samples generally provide more reliable results
- Look for missing groups - A good sample includes all relevant categories from the population
- Question the collection method - Different locations or times might yield different results
Common Mistakes to Avoid
- Don't confuse population with sample - they are different concepts
- Don't assume small samples represent large populations accurately
- Don't ignore obvious sources of bias in sample selection
- Don't choose only convenient or easily accessible subjects for your sample
Key Points to Remember:
- Population is everyone you want to study; sample is the selected group you actually study
- Good samples are representative, large enough, and unbiased to provide reliable conclusions about the population
- The right questions guide everything - they determine what data to collect and how to collect it
- Choose appropriate collection tools - questionnaires for opinions and personal data, recording sheets for tracking events
- Always check for bias - unrepresentative samples lead to incorrect conclusions about the population