Lesson Notes By Weeks and Term v5 - Grade 8

Lesson Video

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.

Performance objectives

• Represent data using pie charts and compound bar graphs.
• Interpret data from various graphs to draw conclusions.
• Calculate and interpret experimental probability.
• Compare theoretical and experimental probability.

Lesson summary

Data handling and probability are essential tools for understanding the world around us. From interpreting election results to understanding the chances of winning the lottery, or even making informed purchasing decisions, these concepts empower us to make sense of information and assess risk. In South Africa, understanding data is crucial for analyzing socioeconomic trends, understanding the impact of government policies, and participating actively in a democratic society. This week, we will focus on representing data using different graphical forms and interpreting data presented in these forms. We'll also solidify our understanding of experimental probability.

Lesson notes

2.1 Representing Data Graphically Pie Charts: Pie charts are circular graphs that are divided into sectors to represent the proportion of different categories in a data set. The entire pie represents 100% of the data, and each sector's size corresponds to the percentage it represents. To create a pie chart, we first need to calculate the angle for each sector using the formula: Angle of sector = (Frequency of category / Total frequency) * 360° Example 1: A survey was conducted among Grade 8 learners at a school in Soweto to determine their favourite type of music.

The results are shown in the table below: | Music Type | Number of Learners | |---|---| | Kwaito | 60 | | Hip Hop | 45 | | Amapiano | 75 | | Gospel | 30 | | Other | 15 | | Total | 225 | Let's create a pie chart to represent this data.

Kwaito: (60/225) 360° = 96° Hip Hop: (45/225) 360° = 72° Amapiano: (75/225) 360° = 120° Gospel: (30/225) 360° = 48° Other: (15/225) 360° = 24° Using these angles, we can draw a pie chart, ensuring each sector is labelled clearly with the music type and its corresponding percentage.

Compound Bar Graphs: Compound bar graphs (also known as stacked bar graphs) are used to compare the composition of different categories. Each bar represents a category, and the bar is divided into sections representing the subcategories within that category.

Example 2: A survey was conducted in three different schools in Cape Town to determine the modes of transport used by learners to get to school.

The results are shown below: | School | Bus | Taxi | Walk | Car | |---|---|---|---|---| | School A | 50 | 30 | 70 | 20 | | School B | 40 | 60 | 50 | 10 | | School C | 60 | 40 | 40 | 30 | To create a compound bar graph, we will have three bars representing School A, School B, and School C. Each bar will be divided into four sections representing the number of learners using Bus, Taxi, Walk, and Car, respectively. A key should be provided to show which colour or pattern represents each mode of transport. 2.2 Interpreting Data Once data is represented graphically, we need to interpret it. This involves drawing conclusions, identifying trends, and answering questions based on the information presented in the graph.

Example 3: Looking at the pie chart from Example 1, we can conclude that Amapiano is the most popular music type among Grade 8 learners in that school (represented by the largest sector), while "Other" is the least popular. We can also calculate percentages from the pie chart to determine the exact proportion of learners who prefer each music type. Looking at the compound bar graph from Example 2, we can compare the modes of transport used by learners in different schools. For example, we can see that a higher number of learners in School C use the bus compared to learners in School B. 2.3 Experimental Probability Experimental probability is the probability of an event occurring based on the results of an experiment.

It is calculated as: Experimental Probability = (Number of times the event occurs / Total number of trials)

Example 4: A coin is tossed 50 times. Heads appears 28 times, and tails appears 22 times. Experimental Probability of getting Heads = 28/50 = 0.56 Experimental Probability of getting Tails = 22/50 = 0.44 Example 5: A bag contains 3 red marbles, 5 blue marbles, and 2 green marbles. An experiment is conducted where a marble is drawn from the bag, its colour is noted, and then the marble is returned to the bag. This is repeated 100 times.

The results are: Red: 32 times Blue: 51 times Green: 17 times Calculate the experimental probability of drawing each color. Experimental Probability of Red = 32/100 = 0.32 Experimental Probability of Blue = 51/100 = 0.51 Experimental Probability of Green = 17/100 = 0.17 2.4 Theoretical vs. Experimental Probability Theoretical probability is what should happen in an ideal situation, while experimental probability is what actually happens when an experiment is conducted. In the coin toss example, the theoretical probability of getting heads is 0.5 (assuming a fair coin).

However, in the experiment, we obtained an experimental probability of 0.

5

6. The difference arises from random chance. As the number of trials increases, the experimental probability tends to get closer to the theoretical probability. Guided Practice (With Solutions)

Question 1: A survey was conducted among 120 learners in a school in Durban to find out their favourite sport.

The results are: Rugby (48), Soccer (36), Cricket (24), Netball (12). Represent this data using a pie chart.

Solution: Calculate the angle for each sport: Rugby: (48/120) 360° = 144° Soccer: (36/120) 360° = 108° Cricket: (24/120) 360° = 72° Netball: (12/120) 360° = 36° Draw a circle and divide it into sectors using the calculated angles. Label each sector with the sport and its corresponding percentage.