Lesson Notes By Weeks and Term v4 - SHS 3
ORGANISING AND REPRESENTING AND INTERPRETING DATA
Download the Lessonotes Mobile Ghana app for faster lesson access on Android and iPhone.
ORGANISING AND REPRESENTING AND INTERPRETING DATA
Download the Lessonotes Mobile Ghana app for faster lesson access on Android and iPhone.
Subject: Additional Mathematics
Class: SHS 3
Term: 2nd Term
Week: 9
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: HANDLING DATA
Subtheme: ORGANISING AND REPRESENTING AND INTERPRETING DATA
This page supports the lesson note with a companion video and a short classroom-ready summary.
For class groups and homework, share this lesson page so learners also get the summary, objectives, and full lesson context.
In our daily lives in Ghana, we often observe relationships between two things. For example, does the amount of rainfall affect the harvest of maize in the Ashanti region? Does the number of hours a student studies affect their WASSCE score? This lesson moves beyond simply observing these relationships. We will learn a powerful mathematical method to find the *exact* straight line that best describes the trend in our data. This "line of best fit" allows us to make educated predictions, which is a vital skill in fields like agriculture, business, engineering, and economics.
2.1. Bivariate Data and Scatter Plots Bivariate Data: This is simply data that has two variables for each observation. We often call them `x` and `y`. For example, for a group of students, we could collect their hours of study (`x`) and their exam scores (`y`). Scatter Plot: A scatter plot is a graph used to display bivariate data. Each pair of values `(x, y)` is plotted as a point on the Cartesian plane. The resulting pattern of points helps us see if there is a relationship, or correlation, between the two variables. Positive Correlation: As `x` increases, `y` tends to increase (points trend upwards). Negative Correlation: As `x` increases, `y` tends to decrease (points trend downwards). No Correlation: The points are scattered randomly with no clear trend. 2.2. The Line of Best Fit
The line of best fit is a straight line that passes through a scatter plot of data points, representing the general trend of the data. It doesn't have to pass through every point, but it should be as close as possible to all the points overall.
Previously, you might have drawn this line "by eye," trying to balance the number of points above and below the line. This method is subjective and can vary from person to person. Today, we learn a precise method. 2.3. The Least Squares Method
This is the mathematical procedure for finding the *best possible* line of best fit. The Main Idea: The method finds a line that minimises the sum of the squares of the vertical distances from each data point to the line. These distances are called residuals. We square the distances so that negative residuals (points below the line) and positive residuals (points above the line) don't cancel each other out. Squaring also gives more weight to points that are further from the line, ensuring the line is pulled towards them.