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: 15
Grade code: 2.4.1.LI.2
Strand code: 4
Sub-strand code: 1
Content standard code: 2.4.1.CS.2
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 last lessons, we learned how to find the "center" of a set of data using the mean, median, and mode. But the center doesn't tell the whole story. Imagine two gari processing businesses in your town. They both sell an average of 50 bags per week. However, one business sells 49, 50, or 51 bags each week, while the other sells 10 bags one week and 90 the next. Which business has a more stable income? To answer this, we need to understand how "spread out" or "dispersed" the data is. This lesson introduces Measures of Dispersion, which are tools that help us measure the consistency, variability, or spread of data.
What is Dispersion? Dispersion (also called variability or spread) tells us how much the individual data points in a set differ from the average value (the mean) and from each other. Low Dispersion: Data points are clustered closely around the mean. This indicates high consistency. (e.g., The daily temperature in a coastal town like Axim). High Dispersion: Data points are spread far apart from the mean. This indicates low consistency or high variability. (e.g., The scores of students in a very difficult test, where some do very well and others do very poorly).
We will study three main measures of dispersion: Variance, Standard Deviation, and Quartile Deviation. A. Variance (s² or σ²)
The variance is the average of the *squared* differences from the Mean. We square the differences so that negative and positive deviations don't cancel each other out, and to give more weight to values that are far from the mean.
Key Distinction: Population vs. Sample Population Variance (σ²): Calculated when you have data for the *entire* group of interest. You divide by the total number of items, N. Sample Variance (s²): Calculated when you only have data for a *part* of the group. You divide by the number of items minus one, n-1. This is called Bessel's correction and it gives a more accurate estimate of the true population variance. In SHS, most problems you encounter will be samples unless stated otherwise.