Section A — Chapters 1–22
Statistics I: Collecting Data
Junior Cycle — 1st Year
- ✓By the end of this lesson students will be able to understand what a statistical investigation involves.
- ✓By the end of this lesson students will be able to distinguish between a population and a sample.
- ✓By the end of this lesson students will be able to differentiate between primary and secondary data.
- ✓By the end of this lesson students will be able to identify various methods of collecting primary data.
- ✓By the end of this lesson students will be able to construct and interpret frequency tables from raw data.
Key concepts
A statistical investigation is a process used to answer a question or solve a problem by collecting, organising, analysing, and interpreting data. It typically involves posing a question, planning how to collect data, collecting the data, organising and representing the data, analysing the data, and finally interpreting the results.
Data refers to facts, figures, or pieces of information collected during a statistical investigation. Data can be numerical (like ages or heights) or categorical (like favourite colours or types of pets).
The population is the entire group of individuals or items that we are interested in studying. For example, if we want to know the average height of all students in Ireland, then all students in Ireland would be the population.
A sample is a smaller, representative group chosen from the population. It is often impractical or impossible to collect data from an entire population, so we collect data from a sample and use it to make inferences about the population. For example, instead of measuring all students in Ireland, we might measure a sample of 1000 students.
Primary data is data that is collected directly by the researcher for a specific purpose. This means the data is original and has not been collected by anyone else before. Examples include data collected through surveys, interviews, or direct observation.
Secondary data is data that has already been collected by someone else and is available for use. This data was originally collected for a different purpose but can be used for a new investigation. Examples include data from government reports, census data, or information found in books or on the internet.
Common methods for collecting primary data include:\n1. **Surveys/Questionnaires**: Asking a set of questions to a group of people.\n2. **Interviews**: Asking questions directly to individuals, often face-to-face or over the phone.\n3. **Observation**: Watching and recording behaviour or events without direct interaction.\n4. **Experiments**: Conducting controlled tests to gather data on cause-and-effect relationships.
Frequency is the number of times a particular value, item, or category appears in a data set. For example, if the number '5' appears three times in a list of numbers, its frequency is 3.
A frequency table is a way of organising raw data by showing how often each item or category occurs. It typically has three columns: one for the item/category, one for tally marks (to help count), and one for the frequency (the total count).
Key facts to remember
- 1A statistical investigation involves collecting, organising, analysing, and interpreting data.
- 2The population is the entire group being studied, while a sample is a smaller, representative part of the population.
- 3Primary data is collected directly by the researcher; secondary data is already available from other sources.
- 4Common methods for collecting primary data include surveys, interviews, observation, and experiments.
- 5Frequency is the count of how many times a particular item or value appears in a data set.
- 6A frequency table organises data using categories, tally marks, and frequencies.
- 7The sum of the frequencies in a frequency table should always equal the total number of observations.
Worked examples
Example 1
A school wants to find out the favourite subject of its 600 students. They decide to ask 60 students from different classes.
Answer
Population: All 600 students in the school.\nSample: The 60 students asked.\nData from their own survey: Primary data.\nData from a national survey: Secondary data.
Understanding the difference between population/sample and primary/secondary data is crucial for statistical investigations.
Example 2
The number of pets owned by 25 students in a 1st Year class is recorded as follows:\n1, 0, 2, 1, 3, 0, 1, 2, 1, 0, 4, 1, 2, 0, 1, 3, 1, 2, 0, 1, 1, 2, 0, 3, 1.\nConstruct a frequency table for this data.
Answer
A frequency table for the number of pets owned by 25 students:\n| Number of Pets | Tally | Frequency |\n|----------------|----------|-----------|\n| 0 | |||| | 6 |\n| 1 | |||| |||| | 10 |\n| 2 | |||| | 5 |\n| 3 | ||| | 3 |\n| 4 | | | 1 |\n| **Total** | | **25** |
Always double-check that the sum of your frequencies equals the total number of data points given in the problem.
Common mistakes
- ✗Confusing the population with the sample, or vice versa.
- ✗Not understanding the difference between primary data (first-hand) and secondary data (already existing).
- ✗Making errors when counting tally marks, leading to incorrect frequencies.
- ✗Forgetting to include a clear title or headings for columns in a frequency table.
- ✗Not checking if the sum of the frequencies matches the total number of data points, which indicates a counting error.
Exam tips
- ★Read the question carefully to determine if you need to identify a population or a sample, or if you are collecting primary or secondary data.
- ★When constructing a frequency table, use tally marks carefully to avoid miscounting. Grouping tallies in fives (|||| ) can help accuracy.
- ★Always sum the frequencies in your table and compare it to the total number of observations given in the problem to catch any counting mistakes.
- ★Ensure your frequency tables are neat, clearly labelled, and easy to read, as presentation is important in maths exams.
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