Lesson Notes By Weeks and Term v4 - SHS 2
STATISTICAL REASONING AND ITS APPLICATION IN REAL LIFE
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STATISTICAL REASONING AND ITS APPLICATION IN REAL LIFE
Download the Lessonotes Mobile Ghana app for faster lesson access on Android and iPhone.
Subject: Mathematics
Class: SHS 2
Term: 2nd Term
Week: 14
Grade code: 2.4.1.LI.2
Strand code: 4
Sub-strand code: 1
Content standard code: 2.4.1.CS.1
Indicator code: 2.4.1.LI.2
Theme: MAKING SENSE OF AND USING DATA
Subtheme: STATISTICAL REASONING AND ITS APPLICATION IN REAL LIFE
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In our daily lives in Ghana, we are constantly surrounded by information used to make decisions. The government uses surveys to decide where to build new schools, businesses in Kejetia or Makola Market use customer feedback to stock goods, and even our school prefects might conduct polls to improve student life. But what if the information they collect is wrong because they asked the questions in a poor way? This lesson is not about calculating statistics, but about the critical first step: ensuring the questions we ask and the methods we use to collect data are fair, clear, and effective.
A. What is a Data Collection Instrument?
A data collection instrument is simply a tool used to gather information. Think of it like a basket for fetching data. If the basket has holes, you will lose some data or get the wrong things. Common instruments include: Questionnaires: A list of written questions that people answer. (e.g., forms you fill out). Interview Guides: A list of questions an interviewer asks in person or over the phone. Observation Checklists: A list of behaviours or events a researcher looks for and ticks off.
The quality of our statistical conclusions depends entirely on the quality of the instrument used to collect the data. This is the principle of "Garbage In, Garbage Out" (GIGO). B. Potential Problems in Data Collection Instruments
Let's explore the "holes in the basket." These are the critical issues we must look for. Bias: This is when a question is phrased in a way that pushes the respondent towards a particular answer. It's unfair and leads to inaccurate results. Leading Questions: These questions suggest the "correct" answer. *Bad Example:* "Don't you agree that the new headmaster's rules are too strict?" (This pressures you to agree). *Good Example:* "To what extent do you agree or disagree with the new headmaster's rules?" (Options: Strongly Agree, Agree, Neutral, Disagree, Strongly Disagree). Loaded Questions: These questions contain an unjustified assumption. *Bad Example:* "Since mobile phones are a major distraction in class, should they be banned completely?" (This assumes they are *always* a major distraction). *Good Example:* "What is your opinion on the impact of mobile phones on learning in the classroom?" Use of Language: The way a question is worded can confuse people or change their answers. Ambiguity (Vagueness): The question is not specific enough. *Bad Example:* "Do you use the internet often?" (What does "often" mean? Daily? Weekly?) *Good Example:* "On a typical day, how many hours do you spend using the internet?" Jargon or Complex Words: Using "big grammar" that respondents may not understand. *Bad Example:* "What is your assessment of the pedagogical effectiveness of the STEM curriculum?" *Good Example:* "Do you think the new STEM curriculum is helping students learn effectively?" Ethical Issues: These concern moral principles and respecting the participants. Privacy & Confidentiality: People have a right to privacy. You must protect their personal information. *Problematic:* A survey asking for a student's name and then asking about their family's income or health issues, without promising to keep the name secret. *Solution:* Make the survey anonymous or clearly state how the data will be kept confidential (e.g., "Your name will not be linked to your answers"). Informed Consent: Participants must know what the study is about and willingly agree to take part. You cannot trick or force them. *Problematic:* Telling students a survey is for "a fun class activity" when it is actually for a report to the GES. *Solution:* Start the survey with a clear statement: "This survey is to gather feedback on the school library to improve its services. Your participation is voluntary." Cultural Sensitivity: Questions must respect the norms, values, and traditions of the community. *Bad Example (in some contexts):* In a rural community, directly asking an elder, "How much money did you make last year?" This can be seen as disrespectful. *Better Approach:* One might ask about general economic well-being through indirect questions, or build trust before asking sensitive questions. For instance, "What are the main sources of livelihood in your household?" Gender: Questions should be inclusive and avoid stereotypes. *Bad Example:* "Please check your father's occupation." (This assumes the father is the primary earner or is present). *Good Example:* "Please check the primary occupation of your guardian(s)." *Another Bad Example:* "For the boys: Do you prefer football or basketball? For the girls: Do you prefer netball or ampe?" (This reinforces stereotypes). *Good Example:* "Which of the following sports do you enjoy? (List all options for everyone)." Practical Considerations: Cost and Time Cost: How much will it cost to conduct the survey? Consider printing costs, transportation to reach people (e.g., travelling to different villages), and data entry. An online survey might be cheaper but excludes people without internet access. Time: How long will it take to collect and analyse the data? A questionnaire with 100 questions is too long and people will not complete it. A face-to-face interview is time-consuming but may yield richer data.