Lesson Notes By Weeks and Term v4 - SHS 1
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 1
Term: 2nd Term
Week: 16
Grade code: 1.4.1.LI.3
Strand code: 4
Sub-strand code: 1
Content standard code: 1.4.1.CS.2
Indicator code: 1.4.1.LI.3
Theme: MAKING SENSE OF AND USING DATA
Subtheme: STATISTICAL REASONING AND ITS APPLICATION IN REAL LIFE
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In Ghana today, we are surrounded by information – from news reports about the economy, to sports statistics for our favourite football teams, to advertisements about which mobile network is the "best". How do we know what to believe? How can we make smart decisions based on this information? This lesson moves beyond just calculating numbers. It teaches us how to use mathematics as a powerful tool for reasoning, making convincing arguments, and making informed choices in our daily lives. We will learn how to look at data critically and use it to support our opinions, whether in a school debate, a family discussion, or a future business decision.
A. What is Statistical Reasoning?
Statistical reasoning is the process of thinking with and about data. It is not just about finding the answer; it's about understanding *why* that is the answer and what it means in the real world. It involves: Examining Data: Looking at the numbers and how they are presented. Analyzing Data: Using mathematical tools (like mean, median) to find patterns and summaries. Making an Inference: An inference is an educated guess or conclusion you draw based on the evidence (the data). Building an Argument: Using your analysis and inference to convince others of your point of view. B. The Right Tool for the Job: Mean, Median, and Mode
To make a good argument, you must use the right mathematical tool. The three most common tools to describe the "centre" of data are the Mean, Median, and Mode. The Mean (or Average): What it is: The sum of all values divided by the number of values. How to calculate: Mean = (Sum of all data points) / (Number of data points) When to use it: The mean is excellent when the data is fairly consistent and doesn't have outliers. An outlier is an extremely high or low value that is very different from the rest of the data. Example: Five friends score the following in a Maths test (out of 20): 15, 16, 14, 17, 15. Sum = 15 + 16 + 14 + 17 + 15 = 77 Number of friends = 5 Mean = 77 / 5 = 15.4. This is a good representation of the group's performance. The Median: What it is: The middle value in a dataset that has been arranged in order (from smallest to largest). How to calculate: Arrange the data in ascending or descending order. If there's an odd number of data points, the median is the single middle value. If there's an even number of data points, the median is the average of the two middle values. When to use it: The median is the best choice when your data has outliers. It is not affected by extremely high or low values. Example: Consider the monthly earnings (in GH₵) of 5 workers at a small chop bar: 400, 450, 500, 550, and 2,500 (the owner's earning). Let's calculate the Mean: (400+450+500+550+2500) / 5 = 4400 / 5 = GH₵ 880. Does this mean the typical worker earns GH₵ 880? No, this is misleading because the owner's high earning (an outlier) has pulled the average up. Now, let's find the Median: Data in order: 400, 450, 500, 550, 2500. The middle value is GH₵ 500. This is a much more accurate and fair representation of what a typical worker at the chop bar earns.
> Teacher's Note: Emphasise this point. The ability to choose between mean and median is a key part of building a strong mathematical argument. Choosing the wrong one can make your argument weak or misleading. The Mode: What it is: The value that appears most frequently in a dataset. When to use it: The mode is useful for categorical data (non-numerical data like colours, brands, etc.) or when you want to know the most popular choice. Example: A survey asks SHS 1 students their favourite brand of sneakers: Nike, Adidas, Puma, Adidas, Nike, Adidas. The mode is Adidas because it appears 3 times, more than any other brand. You would use this to argue which brand a shop near the school should stock the most.