Lesson Notes By Weeks and Term v5 - Grade 9

Lesson Video

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Performance objectives

• Calculate and interpret mean, median, mode, and range.
• Construct and interpret histograms, pie charts, and box-and-whisker plots.
• Determine the probability of single and compound events.
• Apply effective exam preparation strategies.
• Identify common errors in data interpretation.

Lesson summary

This week focuses on reinforcing your understanding of data handling and probability, crucial skills for interpreting the world around you. From understanding election results to predicting the likelihood of rain, these concepts help you make informed decisions. We'll also dedicate time to exam preparation techniques to ensure you're confident and ready to tackle any assessment. Think of data handling as your toolkit for understanding trends and patterns, while probability helps you to quantify uncertainty and make predictions. This is extremely relevant for any career path you might consider, from business and finance to science and technology.

Lesson notes

2.1 Measures of Central Tendency and Dispersion Mean: The average of a set of numbers. Sum all the values and divide by the total number of values.

Formula:* Mean (x̄) = (Sum of all values) / (Number of values) = Σx / n Median: The middle value in a sorted dataset. If there are two middle values (in an even number dataset), the median is the average of those two.

Mode: The value that appears most frequently in a dataset. A dataset can have no mode, one mode (unimodal), or multiple modes (bimodal, multimodal).

Range: The difference between the highest and lowest values in a dataset.

Interquartile Range (IQR): The difference between the upper quartile (Q3) and the lower quartile (Q1). It represents the spread of the middle 50% of the data.

Example 1: A survey was conducted in a Grade 9 class to determine the number of hours students spend studying per week.

The results are: 2, 3, 3, 4, 4, 4, 5, 5, 6,

7. Calculate the mean, median, mode, and range.

Mean: (2 + 3 + 3 + 4 + 4 + 4 + 5 + 5 + 6 + 7) / 10 = 43 / 10 = 4.3 hours Median: First, order the data (already done). Since there are 10 values (even), the median is the average of the 5th and 6th values: (4 + 4) / 2 = 4 hours Mode: The number 4 appears three times, which is more than any other number. So, the mode is 4 hours.

Range: 7 - 2 = 5 hours Example 2: The following data represents the scores of 12 learners on a Mathematics test (out of 50): 25, 30, 32, 35, 38, 40, 42, 45, 45, 47, 48,

5

0. Find the IQ

R. First, find Q1 (the median of the first half of the data): The first half of the data is 25, 30, 32, 35, 38,

4

0. The median of this set is (32+35)/2 = 33.

5. Therefore Q1 = 33.

5. Next, find Q3 (the median of the second half of the data): The second half of the data is 42, 45, 45, 47, 48,

5

0. The median of this set is (45+47)/2 =

4

6. Therefore Q3 =

4

6. IQR = Q3 - Q1 = 46 - 33.5 = 12.5. 2.2 Data Displays Histograms: Used to display the frequency distribution of continuous data. Bars touch each other to indicate a continuous range.

Pie Charts: Used to show the proportion of different categories within a whole. Each slice represents a percentage or fraction of the total. Total angle = 360 degrees.

Box-and-Whisker Plots: Used to display the distribution of data, showing the minimum, maximum, median, Q1, and Q

3. Helps visualize the spread and skewness of the data.

Example 3: Suppose you have data on the ages of people attending a local community event. A histogram would be suitable to show the distribution of age ranges (e.g., 0-10, 11-20, 21-30, etc.). If you wanted to show the percentage of attendees belonging to different ethnic groups, a pie chart would be appropriate.

Example 4: The following data represents the number of hours per week Grade 9 learners spend on social media: 2, 3, 4, 5, 5, 6, 7, 8, 8, 9,

1

0. Draw a box-and-whisker plot to represent the data. Minimum = 2 Maximum = 10 Median = 6 Q1 = 4 Q3 = 8 Draw a number line and mark these five values above it. Draw a box between Q1 and Q3, with a line indicating the median. Draw lines (whiskers) from the box to the minimum and maximum values. 2.3 Probability Probability of an Event: The likelihood that an event will occur.

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

Mutually Exclusive Events: Events that cannot occur at the same time. If events A and B are mutually exclusive, then P(A or B) = P(A) + P(B).

Independent Events: Events where the outcome of one event does not affect the outcome of the other. If events A and B are independent, then P(A and B) = P(A) P(B).

Example 5: What is the probability of rolling a 4 on a standard six-sided die? There is one favorable outcome (rolling a 4). There are six possible outcomes (1, 2, 3, 4, 5, 6). P(rolling a 4) = 1/6 Example 6: A bag contains 3 red balls and 5 blue balls. What is the probability of picking a red ball and then (without replacement) picking another red ball? P(first red ball) = 3/8 After picking one red ball, there are only 2 red balls and 7 total balls left. P(second red ball | first red ball was red) = 2/7 P(red ball and then red ball) = (3/8) (2/7) = 6/56 = 3/28 2.4 Exam Preparation Time Management: Allocate time to each question based on its marks. Don't spend too long on one question.

Question Analysis: Read the question carefully and identify what is being asked. Underline key information.

Revision Techniques: Review notes, practice past papers, and focus on areas of weakness.

Understand Key Concepts: Having a strong understanding of the fundamental concepts will help you to approach questions confidently.

Show your workings: Even if you don't get the final answer correct, you can often get partial marks for showing your working. Guided Practice (With Solutions)

Question 1: The heights (in cm) of 10 learners are: 150, 155, 160, 162, 165, 165, 168, 170, 172,

1

7

5. Calculate the mean and median height.