Lesson Notes By Weeks and Term v4 - SHS 1
ORGANISING, REPRESENTING AND INTERPRETING DATA
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ORGANISING, REPRESENTING AND INTERPRETING DATA
Download the Lessonotes Mobile Ghana app for faster lesson access on Android and iPhone.
Subject: Additional Mathematics
Class: SHS 1
Term: 2nd Term
Week: 15
Grade code: 1.4.1.LI.6
Strand code: 4
Sub-strand code: 1
Content standard code: 1.4.1.CS.1
Indicator code: 1.4.1.LI.6
Theme: HANDLING DATA
Subtheme: ORGANISING, REPRESENTING AND INTERPRETING DATA
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In our daily lives in Ghana, we are surrounded by data. From news reports on Ghana's economy on JoyNews, to statistics about our favourite Black Stars players, to the results of our end-of-term exams. Simply having the numbers is not enough; we need to present this data in a way that is clear, easy to understand, and tells a powerful story. Choosing the right kind of chart or graph is a crucial skill. A good graph can reveal a trend or a comparison instantly, while a poor choice can confuse or even mislead people. This lesson will empower us to become critical thinkers who can not only read graphs but also decide which graph is the most effective tool for any given situation and explain why.
The core of today's lesson is understanding that different types of data require different types of visual representation. Let's explore the main tools in our statistical toolbox. Types of Data
First, we must understand the data we are working with. Categorical Data: Data that can be sorted into distinct groups or categories. Examples: Favourite mobile networks (MTN, Vodafone, AT), regions in Ghana, types of food. Discrete Data: Numerical data that can only take specific, separate values (often whole numbers). Example: Number of students in a class, number of goals scored. Continuous Data: Numerical data that can take any value within a given range. It is often a result of measurement. Examples: Height of students, weight of a bag of maize, time taken to run a race. Bar Chart What it is: A chart that uses rectangular bars of equal width to represent data. The length or height of the bars is proportional to the values they represent. There are gaps between the bars. What it's best for: Comparing values across different categorical or discrete groups. It is excellent for showing "which is more" or "which is less." Key Feature: The distinct gaps between the bars emphasize that the categories are separate and unrelated. Ghanaian Example: A survey was conducted among 50 SHS1 students to find their favourite Ghanaian lunch. The results were: Waakye (20), Jollof Rice (15), Kenkey (10), Banku (5). Why a Bar Chart? The data is categorical (types of food). We want to compare the popularity of each food. A bar chart makes this comparison immediate and easy to see. Waakye would have the tallest bar, and Banku the shortest. Pie Chart What it is: A circular statistical graphic, which is divided into slices (sectors) to illustrate numerical proportion. The size of each slice is proportional to the quantity it represents. What it's best for: Showing parts of a whole. It is perfect when you want to represent data as percentages or fractions of a total. The total must add up to 100% (or the whole). Key Feature: The entire circle represents the total dataset. It's not good for comparing different datasets, only for breaking down one. Ghanaian Example: An SHS student spends their 24-hour day as follows: Sleeping (8 hours), School (8 hours), Studies (3 hours), Chores (2 hours), Leisure (3 hours). Why a Pie Chart? We are looking at how a single entity (a 24-hour day) is broken down into proportions. A pie chart will clearly show what percentage of the day is spent on each activity. For example, School and Sleep would each be a slice representing 8/24 = 1/3 of the circle (120°). Histogram What it is: Similar to a bar chart, but it uses bars to represent the frequency of numerical data that has been grouped into continuous, equal-sized intervals or "bins". What it's best for: Showing the distribution of continuous data. It helps us see the shape of the data – where the values are concentrated, how spread out they are, and if there are any outliers. Key Feature: There are no gaps between the bars, indicating that the data is continuous from one interval to the next. Ghanaian Example: The marks of 50 students in an Additional Mathematics mock exam are grouped as follows. This is the data from the NaCCA exemplar.
| Marks | Frequency | | :--- | :--- | | 1-10 | 2 | | 11-20 | 5 | | 21-30 | 8 | | 31-40 | 8 | | 41-50 | 15 | | 51-60 | 9 | | 61-70 | 3 | Why a Histogram? The data (marks) is continuous and has been grouped into class intervals. A histogram is the perfect tool to show the frequency distribution. It would clearly show that the most common score range is 41-50. A bar chart would be incorrect here because the data is continuous, not separate categories. Line Graph What it is: A graph that uses points connected by lines to show how a value changes. What it's best for: Showing trends or changes over time. It is the best way to visualize how a quantity increases, decreases, or fluctuates. Key Feature: The horizontal x-axis almost always represents a measure of time (hours, days, months, years). Ghanaian Example: The average monthly price of a 50kg bag of cement in Accra over 6 months.
| Month | Price (GHS) | | :--- | :--- | | January | 75 | | February | 78 | | March | 77 | | April | 82 | | May | 85 | | June | 84 | Why a Line Graph? The data shows the change in a single variable (price) over a specific period of time. A line graph will clearly illustrate the upward trend in the price of cement, with a slight dip in June.