Lesson Notes By Weeks and Term v5 - Grade 7

Lesson Video

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Performance objectives

• Represent data using bar graphs, pie charts, and line graphs.
• Calculate and interpret mean, median, and mode.
• Determine the probability of simple events.
• Compare different types of data displays.
• Conduct simple probability experiments.

Lesson summary

Data handling and probability are crucial skills in today's world. In South Africa, understanding data allows us to interpret information presented in newspapers, on television, and online, making informed decisions about everything from political opinions to consumer choices. Probability helps us understand the chances of events happening, which is important in areas like sports betting, understanding weather forecasts, and even assessing risks in our daily lives. This week, we will focus on representing data using different graphs and understanding basic probability concepts.

Lesson notes

2.1 Data Representation Data representation involves organizing and displaying data in a visually appealing and easily understandable format. The most common methods are bar graphs, pie charts, and line graphs.

Bar Graph: A bar graph uses rectangular bars of different heights to represent data values. It's excellent for comparing the frequencies of different categories. The bars can be vertical or horizontal.

Example: Let's say we surveyed 30 Grade 7 learners about their favorite South African dish: Bobotie: 12 learners Biltong: 8 learners Bunny Chow: 6 learners Shisa Nyama: 4 learners We can represent this data using a bar graph. The x-axis would represent the dish types, and the y-axis would represent the number of learners. The height of each bar would correspond to the number of learners who preferred that dish.

Pie Chart: A pie chart (or circle graph) divides a circle into sectors, where each sector represents a proportion of the whole. It’s ideal for showing how different categories contribute to a total. The size of each sector is proportional to the percentage of the data it represents.

Example: Using the same data above, we can create a pie chart. To do this, we need to calculate the percentage of learners who prefer each dish: Bobotie: (12/30) 100% = 40% Biltong: (8/30) 100% = 26.67% (approximately 27%)

Bunny Chow: (6/30) 100% = 20% Shisa Nyama: (4/30) 100% = 13.33% (approximately 13%) The pie chart would then be divided into four sectors representing each dish, with the size of each sector corresponding to the calculated percentages.

Line Graph: A line graph uses points connected by lines to show how data changes over time or another continuous variable. It's useful for showing trends.

Example: Suppose we track the temperature in Johannesburg over a week: Monday: 20°C Tuesday: 22°C Wednesday: 24°C Thursday: 23°C Friday: 21°C Saturday: 25°C Sunday: 26°C We can create a line graph with the days of the week on the x-axis and the temperature on the y-axis. The line will connect the points representing the temperature on each day, showing the temperature trend. 2.2 Measures of Central Tendency Measures of central tendency help describe the center or typical value of a dataset. The most common measures are the mean, median, and mode.

Mean: The mean (or average) is calculated by summing all the values in a dataset and dividing by the number of values.

Example: Suppose we have the following ages of learners in a study group: 12, 13, 12, 14, 13,

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3. The mean age is (12 + 13 + 12 + 14 + 13 + 13) / 6 = 77 / 6 = 12.83 years (approximately).

Median: The median is the middle value in a dataset when the values are arranged in ascending order. If there's an even number of values, the median is the average of the two middle values.

Example: Using the same ages, we arrange them in ascending order: 12, 12, 13, 13, 13,

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4. Since there are 6 values (an even number), the median is the average of the 3rd and 4th values: (13 + 13) / 2 = 13 years.

Mode: The mode is the value that appears most frequently in a dataset.

Example: In the same age data, 13 appears three times, which is more than any other value.

Therefore, the mode is 13 years. 2.3 Probability Probability is the measure of the likelihood that an event will occur. It is expressed as a fraction, decimal, or percentage.

Basic Probability: The probability of an event is calculated as: Probability (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? There is one favorable outcome (rolling a 4) and six possible outcomes (1, 2, 3, 4, 5, 6). Probability (Rolling a 4) = 1/6 Expressing Probability: Probabilities can be expressed as fractions (1/6), decimals (0.1667), or percentages (16.67%).

Example: A bag contains 5 red balls and 3 blue balls. What is the probability of randomly selecting a red ball? There are 5 favorable outcomes (red balls) and 8 total outcomes (5 red + 3 blue). Probability (Selecting a red ball) = 5/8 = 0.625 = 62.5% Guided Practice (With Solutions)

Question 1: A survey was conducted among 25 learners in a Grade 7 class to find out their favorite sport.

The results are as follows: Football: 10, Rugby: 8, Netball: 5, Cricket:

2. Represent this data using a bar graph.

Solution: Draw the axes: Draw a horizontal axis (x-axis) for the sports and a vertical axis (y-axis) for the number of learners.

Label the axes: Label the x-axis with the sports (Football, Rugby, Netball, Cricket) and the y-axis with the number of learners (from 0 to 10, with increments of 1 or 2).

Draw the bars: Draw a bar for each sport, with the height of the bar corresponding to the number of learners who chose that sport.

Football: Bar height = 10 Rugby: Bar height = 8 Netball: Bar height = 5 Cricket: Bar height = 2 Title the graph: Give the graph a title, such as "Favorite Sports of Grade 7 Learners".