Lesson Notes By Weeks and Term v5 - Grade 7
Data handling and probability (Grade 7) – Week 10 focus
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Data handling and probability (Grade 7) – Week 10 focus
Download the Lessonotes Mobile South Africa app for faster lesson access on Android and iPhone.
Subject: Mathematics
Class: Grade 7
Term: Term 4
Week: 10
Theme: General lesson support
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Data handling and probability are crucial skills that allow us to make sense of the world around us. From understanding the spread of diseases in our communities to making informed decisions about our finances, the ability to collect, organise, and interpret data is essential. In South Africa, this is particularly important as we strive to address socio-economic challenges and promote evidence-based decision-making. Understanding probability helps us to assess risks and make reasonable predictions about future events, for example, the likelihood of winning a competition or the chances of rain.
2.1 Data Handling Data Collection: Data is information, and we can collect it in various ways, such as surveys, observations, or experiments.
Data Organisation: Once collected, data needs to be organised, often in tables or tally charts, to make it easier to understand.
Data Representation: We represent data visually using graphs, such as pictograms, bar graphs, and pie charts.
Pictogram: Uses pictures to represent data. Each picture represents a specific quantity.
Example:* If each sun picture represents 5 sunny days, 3 sun pictures would represent 15 sunny days.
Bar Graph: Uses bars of different lengths to represent data. The length of each bar corresponds to the value it represents.
Example:* A bar graph showing the number of learners who prefer different sports.
Pie Chart: A circular chart divided into slices, where each slice represents a proportion of the whole. The size of each slice is proportional to the percentage of the whole it represents.
Example:* A pie chart showing the percentage of learners who walk, take a bus, or are driven to school.
Data Analysis: We analyse data to find patterns and draw conclusions. We use measures of central tendency (mean, median, and mode) and the range to describe and compare data sets.
Mean: The average of a set of numbers. To calculate the mean, add up all the numbers and divide by the total number of numbers.
Example:* Find the mean of the following test scores: 70, 80, 90, 60,
7
5. Mean = (70 + 80 + 90 + 60 + 75) / 5 = 375 / 5 = 75 Median: The middle number in a set of numbers when they are arranged in order from smallest to largest. If there are two middle numbers, the median is the average of those two numbers.
Example:* Find the median of the following numbers: 5, 2, 8, 1,
9. First, arrange the numbers in order: 1, 2, 5, 8,
9. The median is
5. Example:* Find the median of the following numbers: 5, 2, 8, 1, 9,
4. First, arrange the numbers in order: 1, 2, 4, 5, 8,
9. The median is (4 + 5) / 2 = 4.5 Mode: The number that appears most often in a set of numbers. A set of numbers can have no mode, one mode, or more than one mode.
Example:* Find the mode of the following numbers: 2, 3, 3, 4, 5, 3,
6. The mode is 3 (it appears three times).
Range: The difference between the largest and smallest values in a data set.
Example:* Find the range of the following numbers: 1, 5, 2, 8,
9. Range = 9 - 1 = 8 2.2 Probability Probability: The chance that something will happen. It can be expressed as a fraction, decimal, or percentage.
Theoretical Probability: The probability of an event based on mathematical calculations and assumptions. Probability (Event) = (Number of favourable outcomes) / (Total number of possible outcomes)
Experimental Probability: The probability of an event based on the results of an experiment. Experimental Probability (Event) = (Number of times the event occurred) / (Total number of trials)
Possible Outcomes: All the possible results of an event.
Favourable Outcomes: The outcomes we are interested in.
Example: Bar Graph Interpretation: A bar graph shows the number of learners in a class who prefer different types of music: Hip Hop (15 learners), Pop (20 learners), Gospel (10 learners), and Kwaito (5 learners).
Which type of music is most popular?
Answer: Pop
How many learners prefer Hip Hop?
Answer: 15
How many learners are there in the class in total (if all learners have only one preference)?
Answer: 15+20+10+5 = 50
Example: Mean, Median and Mode: The ages of 6 children in a family are 2, 4, 4, 6, 8, and
1
0. Calculate the mean, median, mode, and range of their ages.
Mean: (2 + 4 + 4 + 6 + 8 + 10) / 6 = 34 / 6 = 5.67 (approximately)
Median: Arrange in order: 2, 4, 4, 6, 8,
1
0. The median is (4 + 6) / 2 = 5
Mode: The number that appears most often is
4. Range: 10 - 2 = 8
Example: Probability: A bag contains 3 red balls, 2 blue balls, and 5 green balls. What is the probability of picking a red ball at random?
Total number of balls = 3 + 2 + 5 = 10
Number of red balls = 3
Probability (picking a red ball) = 3/10 = 0.3 = 30%
Guided Practice (With Solutions)
Question 1:
The following table shows the number of houses sold by a real estate agency in Johannesburg over five months:
| Month | Number of Houses Sold |
| --------- | ----------------------- |
| January | 12 |
| February | 15 |
| March | 18 |
| April | 20 |
| May | 15 |