Lesson Notes By Weeks and Term v5 - Grade 7

Lesson Video

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Performance objectives

• Calculate mean, median, mode, and range.
• Compare data sets using these measures.
• Represent probability on a scale from 0 to 1.
• Determine the probability of a single event.

Lesson summary

Data handling and probability are essential skills in mathematics that help us understand the world around us. In South Africa, these skills are particularly important for interpreting information presented in the media, making informed decisions about finances, and understanding social trends. For example, understanding data can help us interpret unemployment statistics, while probability can help us assess the likelihood of winning the Lotto. This week, we'll focus on calculating the mean, median, mode, and range of data sets, and using this knowledge to make comparisons between data sets.

Lesson notes

Measures of Central Tendency and Range Mean: The mean is the average of a set of numbers. To calculate the mean, you add up all the numbers in the set and then divide by the total number of numbers.

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

Median: The median is the middle number in a sorted set of numbers. To find the median, you first need to arrange the numbers in ascending order (from smallest to largest). If there is an odd number of values, the median is the middle value. If there is an even number of values, the median is the average of the two middle values.

Mode: The mode is the number that appears most often in a set of numbers. A data set can have one mode, more than one mode (bimodal or multimodal), or no mode.

Range: The range is the difference between the largest and smallest numbers in a set of numbers.

Formula: Range = Largest value - Smallest value Example 1: Calculating Mean, Median, Mode, and Range Consider the following set of test scores for a Grade 7 Mathematics class: 60, 75, 80, 60, 90, 85, 70, 60, 75,

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5. Mean: Sum of scores = 60 + 75 + 80 + 60 + 90 + 85 + 70 + 60 + 75 + 85 = 740 Number of scores = 10 Mean = 740 / 10 = 74 Explanation:* The average score in the class is

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4. Median: Sorted scores: 60, 60, 60, 70, 75, 75, 80, 85, 85, 90 Since there are 10 scores (an even number), the median is the average of the 5th and 6th scores: (75 + 75) / 2 = 75 Explanation:* Half the class scored 75 or below, and half scored 75 or above.

Mode: The score 60 appears 3 times, which is more than any other score.

Therefore, the mode is

6

0. Explanation:* The most frequent score in the class is

6

0. This may suggest an area where students struggled.

Range: Largest score = 90 Smallest score = 60 Range = 90 - 60 = 30 Explanation:* The scores are spread out over a range of 30 marks.

Example 2: Comparing Data Sets Two Grade 7 classes took a science test.

The scores for Class A are: 55, 65, 70, 75, 80, 85,

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0. The scores for Class B are: 60, 60, 70, 75, 80, 90,

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5. Calculate the mean for each class: Class A: Mean = (55 + 65 + 70 + 75 + 80 + 85 + 90) / 7 = 74.3 Class B: Mean = (60 + 60 + 70 + 75 + 80 + 90 + 95) / 7 = 77.1 Compare the means: Class B has a slightly higher average score than Class

A. This suggests that, on average, Class B performed better on the test.

Probability Probability: Probability is a 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 Scale: A probability scale is a visual representation of probability, ranging from 0 to

1. Calculating Probability: The probability of an event can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes.

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

Example 3: Probability Scale and Calculation Imagine a bag contains 5 red balls, 3 blue balls, and 2 green balls. What is the probability of picking a red ball at random?

Total number of balls: 5 + 3 + 2 = 10 Number of red balls: 5 Probability (picking a red ball) = 5 / 10 = 1/2 = 0.5 On a probability scale, this would be represented halfway between 0 and

1. The event is "likely" but not certain.

Example 4: Understanding Impossible and Certain Events In the example above, the probability of picking a purple ball is 0 (impossible) because there are no purple balls in the bag. The probability of picking either a red, blue, or green ball is 1 (certain) because all the balls are one of these colors. Guided Practice (With Solutions)

Question 1: The ages of 5 children in a family are: 2, 4, 6, 8, and

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0. Calculate the mean, median, mode, and range of their ages.

Solution: Mean: (2 + 4 + 6 + 8 + 10) / 5 = 30 / 5 = 6 Median: The numbers are already in order, so the median is the middle number, which is

6. Mode: There is no mode because each number appears only once.

Range: 10 - 2 = 8

Commentary:* This question reinforces the basic calculations of the measures of central tendency and range. The lack of a mode provides an opportunity to explain when a dataset doesn't have a mode.

Question 2: A coin is flipped once. What is the probability of getting heads? Represent this probability on a probability scale.

Solution: There are two possible outcomes: heads or tails.

There is one favorable outcome: heads. Probability (Heads) = 1 / 2 = 0.5 On a probability scale, this would be represented halfway between 0 and

1. Commentary:* This is a simple probability example to introduce the concept. Emphasize that heads and tails are equally likely outcomes.

Question 3: Two teams, the Lions and the Sharks, played five soccer matches against each other.