Lesson Notes By Weeks and Term v5 - Grade 7

Lesson Video

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Performance objectives

• Construct and interpret pie charts, bar graphs, and histograms.
• Calculate the mean, median, and mode of a data set.
• Determine the probability of a single event.
• Distinguish between certain, likely, unlikely, and impossible events.

Lesson summary

Data handling and probability are essential life skills. We are constantly bombarded with information, and understanding how data is collected, organized, and interpreted helps us make informed decisions. From understanding election polls to comparing prices at different supermarkets, data handling is a powerful tool. Similarly, understanding probability helps us assess risks and make predictions, like estimating our chances of winning a competition or predicting the likelihood of rain. This week we will focus on representing data effectively and understanding basic probability concepts.

Lesson notes

2.1 Data Representation: Data can be represented visually in different ways to make it easier to understand and interpret. The choice of representation depends on the type of data and the message you want to convey.

Bar Graphs: Bar graphs use bars of different lengths to represent the frequency of different categories. They are excellent for comparing data across categories. The x-axis usually represents the categories (e.g., types of fruit, favorite sport). The y-axis represents the frequency (e.g., number of students who like each fruit).

Example: A survey asked Grade 7 learners about their favourite South African sport.

The results were: Football (15), Rugby (10), Cricket (8), Netball (7). A bar graph would clearly show the popularity of each sport.

Histograms: Histograms are similar to bar graphs, but they represent the frequency of data within specific intervals or ranges. They are best used for continuous data (data that can take any value within a range, such as height or temperature). The x-axis represents the intervals (e.g., age ranges: 10-12, 13-15, 16-18). The y-axis represents the frequency (e.g., number of people in each age range).

Example: A survey of the ages of attendees at a local community festival. The data is grouped into age ranges to create a histogram.

Pie Charts: Pie charts represent data as slices of a circle, where the size of each slice is proportional to the percentage of the whole it represents. They are useful for showing the relative proportions of different categories. The entire circle represents 100% of the data. Each slice represents a proportion of the whole.

To calculate the angle of each slice: (Category Frequency / Total Frequency) 360°

Example: A pie chart showing how a family spends their monthly income: Rent (30%), Food (25%), Transport (15%), Education (20%), Entertainment (10%). 2.2 Measures of Central Tendency: These are numbers that describe the "center" of a data set.

Mean: The average of all the numbers in a data set.

To calculate the mean: (Sum of all values) / (Number of values)

Example: The scores of five learners on a math quiz are: 7, 8, 9, 6,

1

0. The mean is (7+8+9+6+10) / 5 = 40 / 5 =

8. Median: The middle number in a data set when the numbers are arranged in order from least to greatest. If there are an even number of values, the median is the average of the two middle numbers.

Example: The ages of seven children are: 5, 7, 3, 8, 6, 9,

4. Ordering them gives: 3, 4, 5, 6, 7, 8,

9. The median is

6. Example (Even): The ages of six children are: 5, 7, 3, 8, 6,

9. Ordering them gives: 3, 5, 6, 7, 8,

9. The median is (6+7)/2 = 6.5 Mode: The number that appears most frequently in a data set. A data set can have one mode, more than one mode (bimodal or multimodal), or no mode.

Example: The number of siblings each of ten learners has are: 1, 2, 0, 1, 3, 2, 1, 0, 1,

2. The mode is 1 (appears four times). 2.3 Probability: Probability is the measure of how likely an event is to occur. It is expressed as a number between 0 and 1, where 0 means the event is impossible, and 1 means the event is certain. Probability of an Event = (Number of Favorable Outcomes) / (Total Number of Possible Outcomes)

Terms: 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 > 0.5).

Example: You are likely to see a car on the road.

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

Example: You are unlikely to win the lottery.

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

Example: A pig flying.

Example: What is the probability of rolling a 4 on a standard six-sided die? Number of favorable outcomes (rolling a 4): 1 Total number of possible outcomes (rolling a 1, 2, 3, 4, 5, or 6): 6 Probability = 1/6 Guided Practice (With Solutions)

Question 1: A class of 30 learners was surveyed about their favourite flavour of Mageu.

The results were: Mango (12), Strawberry (8), Banana (6), and Original (4). Represent this data using a pie chart.

Solution: Calculate the angle for each flavour: Mango: (12/30) 360° = 144° Strawberry: (8/30) 360° = 96° Banana: (6/30) 360° = 72° Original: (4/30) 360° = 48° Draw a circle and divide it into slices with the calculated angles. Label each slice with the flavour and its corresponding percentage (e.g., Mango: 40%).

Mango: (12/30) 100% = 40% Strawberry: (8/30) 100% = 26.7% Banana: (6/30) 100% = 20% Original: (4/30) 100% = 13.3%

Commentary: This question requires learners to apply their understanding of pie charts, including calculating angles and percentages to accurately represent the data.

Question 2: The following are the ages of 10 people in a queue at a spaza shop: 12, 15, 8, 20, 25, 12, 10, 18, 12,

3

0. Calculate the mean, median, and mode of these ages.

Solution: Mean: (12 + 15 + 8 + 20 + 25 + 12 + 10 + 18 + 12 + 30) / 10 = 162 / 10 = 16.2 Median: First, order the data: 8, 10, 12, 12, 12, 15, 18, 20, 25, 30.