Lesson Notes By Weeks and Term v4 - SHS 3
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 3
Term: 2nd Term
Week: 15
Grade code: 3.4.1.LI.2
Strand code: 4
Sub-strand code: 1
Content standard code: 3.4.1.CS.2
Indicator code: 3.4.1.LI.2
Theme: MAKING SENSE OF AND USING DATA
Subtheme: STATISTICAL REASONING AND ITS APPLICATION IN REAL LIFE
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In today's world, we are constantly surrounded by data presented in the news, on social media, and in reports. From Ghana Statistical Service reports on inflation to polls about upcoming elections or even statistics about the performance of the Black Stars, data is used to inform, persuade, and sometimes mislead. This lesson moves beyond just calculating the mean or drawing a bar chart. It focuses on developing the critical thinking skills needed to interpret, question, and draw meaningful conclusions from data presented to us in real life. This skill, known as statistical reasoning, is essential for making informed decisions as a student, a professional, and a responsible Ghanaian citizen.
(Teacher's Note: Begin by asking students where they have recently seen statistics or charts in the news. Examples: COVID-19 updates, football match analysis, reports on the economy on Citi FM/TV or Joy News. This will activate prior knowledge and establish relevance.) A. The Core Idea: Moving from Data to Conclusion
Statistical reasoning is a step-by-step process of thinking with data. It’s not just about the numbers; it’s about what the numbers *mean*.
The Process: Observation: What does the data literally say? This is a direct reading of the facts from the chart or table. *Example:* "The bar for Greater Accra is the tallest." Inference: What can you logically guess or suggest based on the observation? An inference is an educated guess that goes beyond the obvious facts. It is not stated directly in the data but is supported by it. *Example:* "Since the bar for Greater Accra is the tallest, it *suggests* that this region has the highest number of users." Conclusion: What is the overall judgement or decision you can make after considering all observations and inferences? A conclusion is a strong, summary statement that answers a larger question. *Example:* "Based on the data, we can conclude that mobile money services are most prevalent in the Greater Accra Region, likely due to its urban nature and population density." B. Key Definitions Data: A collection of facts, such as numbers, words, measurements, or observations. Data Presentation: The way data is shown visually, e.g., a bar chart, pie chart, line graph, or table. Inference: A logical step of reasoning from what is observed (the data) to what is not explicitly stated but is likely to be true. Key phrases for making inferences are "This suggests that...", "It is likely that...", "This could mean...". Conclusion: A final judgement or summary based on the evidence and inferences. It's the "so what?" of the data. Key phrases for conclusions are "Therefore, we can conclude...", "In summary...", "The evidence shows that...". Justification: The evidence and reasoning you provide to support your conclusion. You must always back up your conclusions with specific points from the data. C. The Critical Thinking Step: Questioning the Data
Before you fully accept a conclusion, you must think like a detective. Ask these questions: Who collected this data? (The source: Ghana Statistical Service? A university? A political party? A media house?) Is the source credible and unbiased? Why was the data collected? (The purpose: To inform the public? To sell a product? To support a political argument?) How was the data collected? (The sample: How many people were asked? Were they representative of the whole population?) For example, a survey of only SHS students in Accra cannot be used to draw conclusions about all Ghanaians. What information is missing? Sometimes, what is *not* shown is as important as what is shown.