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: 17
Grade code: 2.4.1.LI.3
Strand code: 4
Sub-strand code: 1
Content standard code: 2.4.1.CS.2
Indicator code: 2.4.1.LI.3
Theme: MAKING SENSE OF AND USING DATA
Subtheme: STATISTICAL REASONING AND ITS APPLICATION IN REAL LIFE
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This lesson moves beyond just calculating the mean, median, and mode. It focuses on how we can use statistical data to make strong arguments, make smart decisions, and critically evaluate the information we see every day. In Ghana, we are constantly bombarded with data—from news reports about the economy, to social media polls about the best musician, to adverts from MTN and Vodafone claiming to be the best network. This lesson will equip learners with the critical thinking skills to understand, question, and use this data effectively, making them more informed citizens and critical thinkers.
This lesson is about using numbers to think and argue logically. Here are the core ideas we need. a) What is a Statistical Inference? An inference is an educated guess or a conclusion you reach based on evidence and reasoning. In statistics, we use data from a sample to make an inference about a larger population. Example: If we survey 100 students in our school about their favourite banku and tilapia joint, and 70 choose "Auntie Muni's," we can *infer* that Auntie Muni's is likely the most popular joint for the entire school population. This is an inference, not a fact, because we did not ask *every single* student. b) Building a Strong Mathematical Argument A good argument is not just an opinion. It is a conclusion backed by evidence. We can use a simple and powerful structure called CER: Claim, Evidence, Reasoning. Claim: The main point you are trying to make. It is your conclusion or statement. *Example Claim:* "The Black Stars performed better in 2010 than in 2022 at the World Cup." Evidence: The data, facts, or statistics you use to support your claim. Evidence must be specific and relevant. *Example Evidence:* "In the 2010 World Cup, the Black Stars reached the Quarter-Finals, winning 2 games. In the 2022 World Cup, they were eliminated in the Group Stage after winning only 1 game." Reasoning: The explanation that connects your evidence to your claim. It explains *why* the evidence proves your point. *Example Reasoning:* "Reaching the Quarter-Finals is a more advanced stage in the tournament than the Group Stage. Therefore, the evidence of progressing further in 2010 directly supports the claim of a better performance." c) Identifying Bias in Data Bias is a tendency that prevents a data sample from being representative of the whole population. It can make a conclusion unfair or inaccurate. Be a detective and look for these common types of bias: Sampling Bias: This happens when the group you collect data from is not random or diverse enough. *Ghanaian Example:* Imagine a survey asks people in Accra which region has the best food. The results will likely favour Ga-Adangbe dishes. This is biased because it doesn't include the views of people from the Volta, Ashanti, or Northern regions. Misleading Graphs (Visual Bias): The way a graph is drawn can trick you. A common trick is cutting the Y-axis. *Example:* Look at these two graphs showing the same data on the popularity of two phone brands.
Graph B makes the difference between Brand A and Brand B look huge because the vertical axis starts at 40. Graph A gives a more honest picture. Always check if the axis starts at zero! d) Correlation vs. Causation This is a major trap in statistical reasoning. Correlation: Two things happen at the same time or follow the same pattern. Causation: One thing *causes* the other to happen.
Crucial Rule: Correlation does NOT imply causation! Ghanaian Example: In the months of June and July, the sales of umbrellas in Makola Market increase. During the same months, the number of car accidents due to slippery roads also increases. *Correlation:* Umbrella sales and car accidents are correlated; they both go up together. *False Causation:* Does buying an umbrella *cause* car accidents? Of course not! *Real Cause:* A third factor, heavy rainfall, causes both an increase in umbrella sales AND an increase in accidents on slippery roads.
Guided Practice (With Solutions)