Lesson Notes By Weeks and Term v5 - Grade 8
Data handling and probability (Grade 8) – Week 3 focus
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Data handling and probability (Grade 8) – Week 3 focus
Download the Lessonotes Mobile South Africa app for faster lesson access on Android and iPhone.
Subject: Mathematics
Class: Grade 8
Term: Term 4
Week: 3
Theme: General lesson support
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Data handling and probability are essential skills that help us understand and interpret the world around us. In South Africa, these skills are particularly important. For example, understanding data presented in news articles about crime statistics, employment rates, or disease prevalence empowers us to make informed decisions and participate effectively in society. Similarly, understanding probability helps us assess risks and make informed choices in areas like insurance, investments, and even sports betting. This week, we will focus on representing data visually using various graphs and diagrams, and interpreting data to draw conclusions.
2.1 Bar Graphs A bar graph uses rectangular bars to represent data. The length of each bar corresponds to the quantity it represents. Bar graphs are excellent for comparing different categories of data.
Types: Simple bar graphs, dual (or multiple) bar graphs.
Drawing a Bar Graph: Draw and label the axes. The x-axis (horizontal) usually represents categories, and the y-axis (vertical) represents frequencies or quantities. Choose an appropriate scale for the y-axis. The scale should be uniform and cover the entire range of data. Draw bars of equal width for each category. The height of each bar corresponds to the frequency or quantity of that category. Label each bar clearly and provide a title for the graph.
Dual Bar Graph: A dual bar graph compares two sets of data for the same categories. Two bars are drawn side-by-side for each category, representing the two sets of data.
Example 1: A survey was conducted in a Grade 8 class to find out their favourite sports.
The results are shown below: | Sport | Frequency | |--------------|-----------| | Soccer | 15 | | Netball | 10 | | Rugby | 8 | | Athletics | 7 | Draw a bar graph to represent this data.
Solution: Axes: x-axis: Sports; y-axis: Frequency Scale: The maximum frequency is 15, so we can use a scale of 1 unit per increment on the y-axis.
Bars: Draw bars for each sport with heights corresponding to their frequencies.
Labels: Label the axes and give the graph a title (e.g., "Favourite Sports of Grade 8 Students").
Example 2: Dual Bar Graph A school recorded the number of learners who participated in soccer and netball in 2022 and 2023. | | 2022 | 2023 | | ------ | ---- | ---- | | Soccer | 40 | 45 | | Netball | 35 | 40 | Draw a dual bar graph to represent the data.
Solution: Axes: x-axis: Sport, y-axis: Number of Participants Scale: Maximum participants = 45, scale of 5 units per increment works well.
Bars: For each sport, draw two bars next to each other representing 2022 and
2
0
2
3. Use different colors for each year.
Labels: Label the axes, sports, and the years with a legend.
Title: "Soccer and Netball Participation 2022-2023". 2.2 Pie Charts A pie chart (or circle graph) represents data as slices of a circle. The size of each slice is proportional to the quantity it represents. Pie charts are best used to show how different parts contribute to a whole.
Calculating Angle Size: Each category's angle size is calculated as: `(Frequency of category / Total frequency) 360°` Drawing a Pie Chart: Calculate the angle size for each category. Draw a circle using a compass. Use a protractor to draw each slice, starting from the 0° mark. Label each slice with the category and its percentage (Frequency/Total Frequency * 100%). Give the pie chart a title.
Example 3: A survey was conducted to find out the favourite fruits of people in a community.
The results are: | Fruit | Frequency | |------------|-----------| | Apples | 25 | | Bananas | 30 | | Oranges | 15 | | Mangoes | 20 | Draw a pie chart to represent this data.
Solution: Total frequency: 25 + 30 + 15 + 20 = 90 Angle sizes: Apples: (25/90) 360° = 100° Bananas: (30/90) 360° = 120° Oranges: (15/90) 360° = 60° Mangoes: (20/90) 360° = 80° Drawing: Use a compass to draw a circle. Then, use a protractor to measure and draw each slice with the calculated angles.
Labels: Label each slice with the fruit name and the percentage (e.g., Apples: 27.8%).
Title: "Favourite Fruits in the Community". 2.3 Histograms A histogram is a type of bar graph used to represent grouped continuous data (e.g., heights, weights, temperatures). The bars are drawn adjacent to each other (no gaps) to show the continuous nature of the data.
Grouped Data: Data is organized into intervals (e.g., 150-155cm, 155-160cm).
Drawing a Histogram: Draw and label the axes. The x-axis represents the class intervals, and the y-axis represents the frequency. Draw bars for each class interval. The width of the bar corresponds to the interval width, and the height corresponds to the frequency. The bars should touch each other. Label each bar clearly and provide a title for the graph.
Example 4: The heights of 30 students in a class are recorded in centimeters: | Height (cm) | Frequency | |-------------|-----------| | 150-155 | 5 | | 155-160 | 8 | | 160-165 | 10 | | 165-170 | 7 | Draw a histogram to represent this data.
Solution: Axes: x-axis: Height (cm); y-axis: Frequency Bars: Draw bars for each height interval with heights corresponding to their frequencies. Make sure the bars touch.
Labels: Label the axes and give the graph a title (e.g., "Heights of Students in a Class"). 2.4 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 5: A coin is tossed 50 times. Heads appears 28 times. What is the experimental probability of getting heads?