Lesson Notes By Weeks and Term v5 - Grade 8

Lesson Video

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Performance objectives

• Calculate the probability of a single event (as a fraction, decimal, and percentage).
• Construct and interpret frequency tables and bar graphs.
• Determine the range, mode, median, and mean of a data set.
• Solve real-world problems involving data and probability.

Lesson summary

This week, we delve into the fascinating world of data handling and probability. In South Africa, understanding data and probability is crucial for making informed decisions in various aspects of life, from understanding crime statistics in your neighbourhood to predicting weather patterns that affect agriculture. Learning how to collect, organise, analyse, and interpret data empowers you to become a critical thinker and problem-solver.

Furthermore, grasping probability concepts will help you understand risks and opportunities in games of chance, business ventures, and even health decisions.

Lesson notes

2.1 Probability: Probability is the measure of the likelihood that an event will occur. It is expressed as a number between 0 and 1, where 0 represents impossibility and 1 represents certainty.

Event: An event is a specific outcome or set of outcomes in a situation. For example, rolling a 6 on a die is an event.

Sample Space: The sample space is the set of all possible outcomes. For example, the sample space of rolling a die is {1, 2, 3, 4, 5, 6}.

Calculating Probability: The probability of an event occurring is calculated as: Probability (Event) = (Number of favourable outcomes) / (Total number of possible outcomes) We can express probabilities as fractions, decimals, or percentages.

Fraction: e.g., 1/6 Decimal: e.g., 0.167 Percentage: e.g., 16.7% Example 1: What is the probability of drawing a red ball from a bag containing 3 red balls, 2 blue balls, and 5 green balls? Number of red balls (favourable outcomes) = 3 Total number of balls (total possible outcomes) = 3 + 2 + 5 = 10 Probability (Red ball) = 3/10 = 0.3 = 30% Example 2: A fair coin is flipped. What is the probability of getting heads? Number of heads (favourable outcomes) = 1 Total number of outcomes (heads or tails) = 2 Probability (Heads) = 1/2 = 0.5 = 50% 2.2 Data Representation: Data representation involves organising and displaying data in a clear and understandable manner.

Common methods include: Frequency Tables: A frequency table lists each data value and how often it occurs.

Example: A survey of favourite fruits among Grade 8 learners yielded the following results: Apples: 10, Bananas: 15, Oranges: 8, Grapes:

7. Frequency Table: | Fruit | Frequency | | ------- | --------- | | Apples | 10 | | Bananas | 15 | | Oranges | 8 | | Grapes | 7 | Bar Graphs: A bar graph uses bars of different heights to represent data. The height of each bar corresponds to the frequency of the data value it represents.

X-axis: Fruit Type, Y-axis: Frequency Pie Charts: A pie chart is a circular graph that divides a circle into slices to represent proportions of data. Each slice represents a percentage of the whole. Often used to show relative proportions of different categories.

To calculate the angle for each slice: (Frequency/Total Frequency) x 360° For the above example: Apples: (10/40) x 360° = 90° Bananas: (15/40) x 360° = 135° Oranges: (8/40) x 360° = 72° Grapes: (7/40) x 360° = 63° 2.3 Measures of Central Tendency: Measures of central tendency describe the "center" of a data set.

Mean: The mean is the average of all the data values. Mean = (Sum of all data values) / (Number of data values)

Median: The median is the middle value when the data is arranged in order. If there are two middle values, the median is the average of those two.

Mode: The mode is the data value that occurs most frequently. A data set can have no mode, one mode, or multiple modes.

Range: The range is the difference between the largest and smallest data values. Range = Largest value - Smallest Value Example 3: Consider the following test scores: 60, 70, 70, 80, 90 Mean = (60 + 70 + 70 + 80 + 90) / 5 = 370 / 5 = 74 To find the median, order the data: 60, 70, 70, 80,

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0. The median is

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0. The mode is 70 because it appears twice. Range = 90 - 60 = 30 Guided Practice (With Solutions)

Question 1: A bag contains 4 blue marbles, 5 red marbles, and 1 green marble. What is the probability of drawing a blue marble? Express your answer as a fraction, decimal, and percentage.

Solution: Number of blue marbles (favourable outcomes) = 4 Total number of marbles (total possible outcomes) = 4 + 5 + 1 = 10 Probability (Blue marble) = 4/10 = 2/5 = 0.4 = 40% Question 2: The following are the ages of students in a Grade 8 class: 13, 14, 13, 15, 14, 13, 14, 14, 15,

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3. Construct a frequency table for this data.

Solution: | Age | Frequency | | --- | --------- | | 13 | 4 | | 14 | 4 | | 15 | 2 | Question 3: Using the data from Question 2, calculate the mean, median, mode, and range of the ages.

Solution: Mean = (13 + 14 + 13 + 15 + 14 + 13 + 14 + 14 + 15 + 13) / 10 = 138/10 = 13.8 To find the median, order the data: 13, 13, 13, 13, 14, 14, 14, 14, 15,

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5. The two middle numbers are 14 and

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4. So, the median = (14 + 14)/2 = 14 Mode = 13 and 14 (Bimodal – occurring equally and most frequently) Range = 15 - 13 = 2 Independent Practice (Questions Only) A spinner has 8 equal sections, numbered 1 to

8. What is the probability of landing on an even number? Express the answer as a simplified fraction. In a survey of 30 students, 12 said their favourite subject was Maths, 8 said English, 6 said Science, and 4 said History. Create a frequency table to represent this data. Represent the data from question 2 using a bar graph. The following are the heights (in cm) of 10 learners: 150, 155, 160, 152, 158, 155, 162, 150, 155,

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0. Calculate the mean, median, mode, and range of the heights. A box contains 20 chocolates. 8 are milk chocolate, 7 are dark chocolate, and 5 are white chocolate.