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: 16
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 constantly surrounded by information, or 'data'. This could be the prices of foodstuffs at Makola Market, the performance of the Black Stars, the number of people using different mobile networks, or even the rainfall patterns in our region. To make sense of all this information, we need to organise and represent it visually. Choosing the *right* way to show the data is a powerful skill. A good chart can make a complex point clear and convincing, while a poor choice can be confusing or even misleading.
This lesson focuses on understanding *when* and *why* to use specific types of charts. The main types we will compare are: Bar Charts, Pie Charts, Histograms, and Line Graphs. A. The Bar Chart What is it? A chart that uses rectangular bars of equal width to represent data. The length of each bar is proportional to the value it represents. The bars do not touch each other. When to Use It: To compare distinct, separate categories of data (categorical data). To show the frequency or quantity of different items. Examples: Comparing the number of subscribers for MTN, Vodafone, and AT; showing the favourite subjects of students in a class; comparing the number of goals scored by different players. Strengths: Very easy to read and understand at a glance. Excellent for making direct comparisons between categories. Clearly shows which category is the largest or smallest. Weaknesses: Not suitable for showing trends over time or parts of a whole. Can become cluttered if there are too many categories. Ghanaian Example: A survey was conducted to find the most popular local dish among SHS 1 students. Jollof Rice: 45 students Waakye: 30 students Banku and Tilapia: 25 students Fufu and Soup: 15 students
A bar chart is perfect here because we are comparing four distinct categories (dishes). We can easily see that Jollof is the most popular. B. The Pie Chart What is it? A circular chart divided into slices, where each slice represents a proportion or percentage of the whole. The total of all slices must be 100%. When to Use It: To show how a whole is divided into parts (composition). When you want to represent data as percentages. Examples: Breakdown of a family's monthly budget (food, rent, transport, savings); showing the percentage of different ethnic groups in a region; representing the proportion of votes each candidate received in an SRC election. Strengths: Visually intuitive for showing part-to-whole relationships. Excellent for displaying percentages and proportions. Weaknesses: Difficult to compare the exact sizes of slices, especially if they are similar. Becomes ineffective and hard to read with more than 5-6 categories. Not suitable for showing changes over time. Ghanaian Example: A student spends their weekly pocket money of GHS 50 as follows: Trotro Fare: GHS 15 (30%) Lunch: GHS 20 (40%) Airtime: GHS 10 (20%) Savings: GHS 5 (10%)
A pie chart is ideal because it clearly shows the proportion of the student's total money spent on each category. C. The Histogram What is it? A chart that looks similar to a bar chart, but is used for continuous data that has been grouped into intervals or "bins". The bars have no gaps between them to show that the data is continuous. The area of each bar is proportional to the frequency. When to Use It: To show the distribution of continuous numerical data. To see the shape of the data (e.g., is it symmetric, skewed?). Examples: Distribution of students' heights in a school (e.g., 150-155 cm, 155-160 cm, etc.); distribution of scores in an end-of-term exam; showing the age distribution of people in a community. Strengths: Excellent for visualizing the frequency distribution of a large dataset. Helps to identify the concentration of data, gaps, and outliers. Weaknesses: Cannot read exact values as data is grouped into intervals. The appearance of the histogram can change significantly if you change the width of the intervals. Ghanaian Example: The scores of 50 students in an Additional Mathematics test (out of 100) are grouped as follows: 40-49: 5 students 50-59: 12 students 60-69: 18 students 70-79: 10 students 80-89: 5 students
A histogram is the correct choice because the scores are continuous numerical data grouped into intervals. A bar chart would be wrong here because the data is continuous, not separate categories. D. The Line Graph What is it? A chart that uses points connected by lines to show how a value changes over a continuous interval, most commonly time. When to Use It: To track changes or trends over a period of time. To compare how multiple variables change over the same time period. Examples: Tracking the exchange rate of the Ghana Cedi to the US Dollar over a year; showing the change in monthly rainfall in Accra; plotting a patient's temperature over several hours. Strengths: Excellent for showing trends, patterns, acceleration, or deceleration. Can be used to compare multiple datasets easily on the same axes. Weaknesses: Only suitable for data where the points have a natural order, like time. Can be misleading if the scale on the axes is not chosen carefully. Ghanaian Example: The average monthly price of a 50kg bag of maize in Kumasi Central Market in 2022. Jan: GHS 250 Feb: GHS 260 Mar: GHS 280 Apr: GHS 275 ...and so on for 12 months.