Lesson Notes By Weeks and Term v5 - Grade 8

Lesson Video

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Performance objectives

• Collect and organize data using tally marks and frequency tables.
• Represent data using bar graphs, histograms, and pie charts.
• Calculate and interpret mean, median, and mode.
• Determine the probability of a single event.
• Express probability as a fraction, decimal, and percentage.

Lesson summary

Data handling and probability are essential skills for understanding the world around us. In South Africa, from understanding census data to interpreting election results or making informed decisions about investments, these skills are crucial. Businesses use data to understand customer preferences, and the government uses data to plan services and policies. Probability helps us assess risk and make predictions, like the likelihood of rainfall for farming or the chances of winning a competition. This week, we will focus on collecting, organizing, representing, and interpreting data using various methods, as well as calculating and understanding basic probabilities.

Lesson notes

2.1 Data Collection and Organization: Data is a collection of facts, figures, or information. We collect data to analyze and draw conclusions. A simple way to collect data is using tally marks. A tally mark is a vertical line used to count items. After every four tally marks, the fifth is drawn across the previous four, creating a group of five, which makes counting easier. A frequency table then summarizes the data, showing how many times each value occurs.

Example: Let's say we survey 30 Grade 8 learners about their favorite sport: Soccer, Rugby, Cricket, or Netball. | Sport | Tally Marks | Frequency | | -------- | ----------- | --------- | | Soccer | IIII IIII IIII | 12 | | Rugby | IIII II | 7 | | Cricket | IIII I | 6 | | Netball | IIII | 5 | | Total | | 30 | 2.2 Data Representation: Bar Graphs: Use bars of different heights to represent the frequency of different categories. The height of each bar corresponds to the frequency.

Histograms: Similar to bar graphs, but used for grouped data. The bars touch each other to show that the data is continuous. The width of each bar represents a class interval, and the height represents the frequency of that interval.

Pie Charts: A circle divided into sectors, where each sector represents a proportion of the whole. The angle of each sector is proportional to the frequency of the corresponding category. Pie charts are useful for showing the relative sizes of different parts of a whole.

Example (using the sport data): Bar Graph: (Imagine a bar graph with the x-axis showing the sports and the y-axis showing the frequency. The soccer bar would be the tallest, followed by rugby, then cricket, then netball).

Histogram: (Not applicable in this case as the data isn't grouped. Histograms are used for continuous data like height or weight).

Pie Chart: To create a pie chart, we calculate the angle for each sport. A full circle is 360 degrees.

Soccer: (12/30) 360 = 144 degrees Rugby: (7/30) 360 = 84 degrees Cricket: (6/30) 360 = 72 degrees Netball: (5/30) 360 = 60 degrees 2.3 Measures of Central Tendency: Mean: The average of a set of numbers. To calculate the mean, add up all the numbers and divide by the total number of values.

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

Median: The middle value in a set of numbers that are arranged in order from least to greatest. If there are two middle numbers, the median is the average of those two numbers.

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

Example: Consider the following ages of 7 people in a family: 5, 8, 10, 12, 15, 40,

4

2. Mean: (5 + 8 + 10 + 12 + 15 + 40 + 42) / 7 = 132 / 7 = 18.86 (approximately)

Median: First, we arrange the numbers in order (they already are). The middle number is

1

2. So, the median is

1

2. Mode: No number appears more than once. So, there is no mode. 2.4 Probability: Probability is the measure of how likely an event is to occur. It is expressed as a fraction, decimal, or percentage. The probability of an event is always between 0 and 1 (or 0% and 100%).

Formula: Probability of an event = (Number of favorable outcomes) / (Total number of possible outcomes)

Example: What is the probability of rolling a 4 on a standard six-sided die?

Number of favorable outcomes: 1 (rolling a 4)

Total number of possible outcomes: 6 (1, 2, 3, 4, 5, 6) Probability = 1/6 To express as a decimal: 1/6 = 0.1667 (approximately)

To express as a percentage: 0.1667 * 100 = 16.67% (approximately) Guided Practice (With Solutions)

Question 1: A bag contains 5 red marbles, 3 blue marbles, and 2 green marbles. What is the probability of randomly selecting a blue marble? Express your answer as a fraction, decimal, and percentage.

Solution: Number of favorable outcomes (blue marbles): 3 Total number of possible outcomes (total marbles): 5 + 3 + 2 = 10 Probability (blue marble) = 3/10 Decimal: 3/10 = 0.3 Percentage: 0.3 100 = 30%

Commentary: This question tests the basic understanding of probability calculation. Make sure to identify the favorable outcome and the total possible outcomes correctly.* Question 2: The following data represents the number of hours 20 learners spend studying each week: 2, 3, 4, 2, 5, 3, 2, 4, 6, 2, 3, 4, 5, 2, 3, 3, 4, 5, 2,

4. Find the mode, median, and mean.

Solution: Mode: The value that appears most often is 2 (appears 5 times). So, the mode is

2. Median: First, arrange the numbers in order: 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5,

6. There are 20 numbers, so the median is the average of the 10th and 11th numbers. The 10th number is 3, and the 11th number is

4. The average is (3+4)/2 = 3.

5. So, the median is 3.

5. Mean: (2+3+4+2+5+3+2+4+6+2+3+4+5+2+3+3+4+5+2+4) / 20 = 68 / 20 = 3.4

Commentary: This question tests the ability to calculate the three measures of central tendency.