Lesson Notes By Weeks and Term v5 - Grade 7

Lesson Video

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Performance objectives

• Interpret data from graphs, charts, and tables.
• Calculate the mean, median, and mode of a data set.
• Determine the range of a data set.
• Describe and express the probability of simple events.

Lesson summary

Data handling and probability are essential skills in mathematics that help us understand and interpret the world around us. In South Africa, understanding data is crucial for making informed decisions about everything from national elections to understanding crime statistics in our local communities. Probability helps us assess risks, predict outcomes, and make informed choices in everyday situations. This week, we will be focusing on interpreting and analyzing data displayed in various forms, as well as understanding basic probability concepts.

Lesson notes

2.1 Interpreting Data Displays Data can be presented in different ways to make it easier to understand. The most common types of data displays are bar graphs, pie charts, pictograms, and tables.

Bar Graphs: Bar graphs use bars of different lengths to represent data. The length of each bar corresponds to the value it represents. Bar graphs are useful for comparing data across different categories.

Example: A bar graph shows the number of learners who prefer different sports: Soccer (25), Netball (15), Rugby (10), and Athletics (20). To interpret this graph, look at the height of each bar. Soccer is the most popular, and Rugby is the least popular.

Pie Charts: Pie charts are circular charts divided into "slices." Each slice represents a proportion of the whole. Pie charts are good for showing how a whole is divided into parts, often displayed as percentages.

Example: A pie chart shows the percentage of households in a town using different types of fuel for cooking: Electricity (50%), Gas (30%), Paraffin (15%), and Wood (5%). The largest slice (50%) represents electricity.

Pictograms: Pictograms use pictures or symbols to represent data. Each picture represents a specific quantity.

Example: A pictogram shows the number of cars sold by a dealership each month. If each car symbol represents 10 cars, and there are 5 car symbols for January, then 50 cars were sold in January.

Tables: Tables organize data in rows and columns. They are useful for presenting precise data and for comparing different sets of data.

Example: A table shows the temperatures recorded in different cities in South Africa: | City | Temperature (°C) | | --------- | ---------------- | | Cape Town | 25 | | Durban | 28 | | Johannesburg| 22 | | Pretoria | 24 | 2.2 Measures of Central Tendency Measures of central tendency are used to find a "typical" value for a set of data.

The three main measures are: Mean (Average): The sum of all the values in the data set divided by the number of values.

Example: Find the mean of the following test scores: 70, 80, 90, 60,

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5. Sum: 70 + 80 + 90 + 60 + 75 = 375 Number of values: 5 Mean: 375 / 5 = 75 Median: The middle value when the data set is arranged in order from smallest to largest (or largest to smallest). If there are two middle values, the median is the mean of these two values.

Example 1: Find the median of the following ages: 10, 12, 15, 11,

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3. Order: 10, 11, 12, 13, 15 Median: 12 Example 2: Find the median of the following heights (cm): 140, 150, 145,

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5. Order: 140, 145, 150, 155 Middle values: 145 and 150 Median: (145 + 150) / 2 = 147.5 Mode: The value that appears most frequently in the data set. A data set can have no mode, one mode, or multiple modes.

Example: Find the mode of the following shoe sizes: 6, 7, 7, 8, 9, 7,

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0. The value 7 appears three times, which is more than any other value.

Mode: 7 2.3 Range The range is the difference between the largest and smallest values in a data set. It indicates the spread of the data.

Example: Find the range of the following temperatures (°C): 20, 22, 25, 18,

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7. Largest value: 27 Smallest value: 18 Range: 27 - 18 = 9 2.4 Probability Probability is the chance that an event will occur. We can describe probability using words like "certain," "likely," "unlikely," and "impossible." We can also express probability as a fraction.

Certain: The event will definitely happen. Probability = 1 (or 100%).

Example: The sun will rise tomorrow.

Likely: The event is more likely to happen than not. Probability is closer to

1. Example: If you flip a fair coin, getting heads is likely after many trials.

Unlikely: The event is less likely to happen than not. Probability is closer to

0. Example: Winning the lottery.

Impossible: The event cannot happen. Probability =

0. Example: A cow flying to the moon.

Expressing Probability as a Fraction: Probability can be expressed as: Probability = (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 (rolling a 4): 1 Total number of possible outcomes (rolling a 1, 2, 3, 4, 5, or 6): 6 Probability = 1/6 Comparing Probabilities: We can compare probabilities to determine which event is more or less likely to occur. A larger fraction represents a higher probability.

Example: Which is more likely: rolling an even number on a six-sided die or rolling a number greater than 4? Rolling an even number (2, 4, 6): Probability = 3/6 = 1/2 Rolling a number greater than 4 (5, 6): Probability = 2/6 = 1/3 Since 1/2 is greater than 1/3, rolling an even number is more likely. Guided Practice (With Solutions)

Question 1: The following bar graph shows the number of people who visited the Kruger National Park in different months: January (500), February (400), March (300), April (600), May (700). Which month had the most visitors?

Solution: Looking at the bar graph, the bar for May is the tallest, representing 700 visitors.