Lesson Notes By Weeks and Term v5 - Grade 8

Lesson Video

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Performance objectives

• Calculate and interpret mean, median, and mode.
• Represent data using appropriate graphs.
• Interpret data from various graphs.
• Determine the probability of a single event.
• Distinguish between certain, likely, unlikely, and impossible events.

Lesson summary

Data handling and probability are essential skills in the 21st century. We are constantly bombarded with information – from news reports to social media feeds to advertisements. Understanding how data is collected, organised, represented, and interpreted allows us to make informed decisions and avoid being misled. Probability helps us assess the likelihood of events, which is crucial in fields like finance, medicine, and even everyday activities like deciding whether to take an umbrella to school or invest in a stokvel.

Lesson notes

2.1 Measures of Central Tendency Measures of central tendency are single values that attempt to describe a set of data by identifying the "central" position within that set.

The three most common measures are: Mean (Average): The sum of all the values in a data set divided by the number of values.

Formula: Mean = (Sum of all values) / (Number of values)

Median: The middle value in a data set when the values are arranged in ascending (smallest to largest) order. If there is an even number of values, the median is the average of the two middle values.

Mode: The value that appears most frequently in a data set. A data set can have one mode (unimodal), more than one mode (bimodal, multimodal), or no mode.

Example 1: Calculating Mean, Median and Mode A survey was conducted in a Grade 8 class to determine the number of hours each student spends on homework per week.

The following data was collected: 2, 3, 2, 4, 5, 2, 3, 1, 0, 2, 4, 3 Mean: (2 + 3 + 2 + 4 + 5 + 2 + 3 + 1 + 0 + 2 + 4 + 3) / 12 = 31 / 12 ≈ 2.58 hours Median: First, arrange the data in ascending order: 0, 1, 2, 2, 2, 2, 3, 3, 3, 4, 4, 5 Since there are 12 values (even number), the median is the average of the 6th and 7th values: (2 + 3) / 2 = 2.5 hours Mode: The value 2 appears most frequently (4 times).

Therefore, the mode is 2 hours. 2.2 Data Representation Different types of graphs are suitable for representing different types of data.

Some common graphs include: Bar Graph: Used to compare categorical data (data that can be divided into groups). The height of each bar represents the frequency or amount of each category.

Pie Chart: Used to show the proportion of each category relative to the whole. Each slice of the pie represents a category, and the size of the slice is proportional to the percentage of that category.

Histogram: Used to represent continuous data (data that can take on any value within a range) that has been grouped into intervals (bins). Similar to a bar graph, but the bars are adjacent to each other to show the continuous nature of the data.

Example 2: Choosing the Right Graph Suppose we want to represent the following data about the favourite sports of Grade 8 learners: Soccer: 45 Rugby: 30 Netball: 20 Cricket: 15 A bar graph would be a good choice to compare the popularity of each sport. A pie chart would be suitable to show the percentage of learners who prefer each sport out of the total number of learners surveyed. A histogram would not be appropriate since the data is categorical (sports), not continuous. 2.3 Interpretation of Graphs Interpreting graphs involves extracting meaningful information from them. This includes identifying trends, comparing categories, and drawing conclusions based on the data presented.

Key aspects to consider are: titles, labels on axes, scales, and overall shape or pattern of the graph.

Example 3: Interpreting a Bar Graph Imagine a bar graph showing the number of reported crime incidents in different areas of a city in

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3. If the bar for "Area A" is significantly taller than the bars for other areas, we can conclude that Area A had a higher number of reported crime incidents than other areas in 2023. 2.4 Basic Probability Probability is the measure of how likely an event is to occur. The probability of an event is a number between 0 and 1, where 0 means the event is impossible, and 1 means the event is certain.

Classical Definition of Probability: If all outcomes of an experiment are equally likely, then the probability of an event A is: P(A) = (Number of favourable outcomes for A) / (Total number of possible outcomes)

Example 4: Calculating Probability A bag contains 5 red marbles and 3 blue marbles. What is the probability of randomly selecting a red marble? Number of favourable outcomes (red marbles) = 5 Total number of possible outcomes (total marbles) = 5 + 3 = 8 P(Red) = 5/8 2.5 Certain, Likely, Unlikely, and Impossible Events These terms describe the likelihood of an event occurring: Certain: The event will definitely happen (probability = 1).

Example: The sun will rise tomorrow.

Likely: The event is more likely to happen than not (probability greater than 0.5).

Example: Picking a vowel from the letters of the word "PROBABILITY".

Unlikely: The event is less likely to happen than not (probability less than 0.5).

Example: Winning the lottery.

Impossible: The event cannot happen (probability = 0).

Example: Rolling a 7 on a standard 6-sided die. Guided Practice (With Solutions)

Question 1: The marks obtained by 10 learners in a Mathematics test (out of 50) are: 35, 40, 32, 45, 38, 42, 35, 30, 40,

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5. Calculate the mean, median, and mode of these marks.

Solution: Mean: (35 + 40 + 32 + 45 + 38 + 42 + 35 + 30 + 40 + 35) / 10 = 352 / 10 = 35.2 Median: Arrange the marks in ascending order: 30, 32, 35, 35, 35, 38, 40, 40, 42, 45 The median is the average of the 5th and 6th values: (35 + 38) / 2 = 36.5 Mode: The mark 35 appears most frequently (3 times).

Therefore, the mode is 35.