Lesson Notes By Weeks and Term v5 - Grade 7

Lesson Video

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Performance objectives

• Construct and interpret pie charts and bar graphs.
• Calculate mean, median, and mode for a data set.
• Determine the probability of a simple event.
• Compare different data sets.
• Design and conduct a simple probability experiment.

Lesson summary

Data handling and probability are essential skills in our daily lives. From interpreting news reports about crime statistics in Gauteng to understanding the likelihood of winning the Lotto, these concepts help us make informed decisions. This week, we will focus on expanding our understanding of data representation, analysis, and the basics of probability. These skills are invaluable, helping us interpret the world around us critically and quantitatively. We'll also explore how data is used to improve things like service delivery and resource allocation in our communities.

Lesson notes

2.1 Data Representation: Pie Charts and Bar Graphs Pie Charts: Pie charts are circular diagrams divided into sectors, where each sector represents a proportion of the whole. The size of each sector is proportional to the quantity it represents. The entire circle represents 100%. They are excellent for showing the relative sizes of different categories.

Construction: To construct a pie chart, we need to calculate the angle of each sector. If we have a category representing a certain percentage of the total, the angle of the sector is (percentage/100) 360°.

Interpretation: Pie charts help us quickly visualize which category contributes the most or the least to the whole.

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

Construction: We need to choose appropriate scales for the axes. One axis represents the categories, and the other represents the values. The bars should be of uniform width and clearly labeled.

Interpretation: Bar graphs make it easy to compare the values of different categories at a glance.

Example 1: Pie Chart A survey was conducted in a Grade 7 class to determine their favourite South African music genre.

The results are as follows: Amapiano: 15 students Gqom: 10 students Hip Hop: 5 students Construct a pie chart to represent this data.

Solution: Calculate the total number of students: 15 + 10 + 5 = 30 students Calculate the percentage for each genre: Amapiano: (15/30) 100% = 50% Gqom: (10/30) 100% = 33.33% (approx. 33%)

Hip Hop: (5/30) 100% = 16.67% (approx. 17%)

Calculate the angle for each sector: Amapiano: (50/100) 360° = 180° Gqom: (33/100) 360° = 118.8° (approx. 119°)

Hip Hop: (17/100) 360° = 61.2° (approx. 61°) Draw a circle and divide it into sectors with the calculated angles. Label each sector clearly with the genre and percentage.

Example 2: Bar Graph The number of tourists visiting Kruger National Park from different provinces in South Africa during a particular month is as follows: Gauteng: 5000 Limpopo: 3000 Mpumalanga: 4000 KwaZulu-Natal: 2000 Construct a bar graph to represent this data.

Solution: Draw the axes: The horizontal axis represents the provinces, and the vertical axis represents the number of tourists (choose a suitable scale, e.g., 1 cm = 1000 tourists).

Draw the bars: Draw a bar for each province with a height corresponding to the number of tourists. Label each bar clearly. 2.2 Measures of Central Tendency: Mean, Median, and Mode These measures help us summarize a set of data using a single value.

Mean: The mean is the average of all the values in the dataset. It's calculated by adding all the values and dividing by the number of values.

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

Median: The median is the middle value in a dataset when the values are arranged in ascending order. If there are two middle values, the median is the average of those two values.

Mode: The mode is the value that appears most frequently in a dataset. A dataset can have no mode, one mode, or multiple modes.

Example 3: Mean, Median, and Mode The scores of 8 learners on a mathematics test (out of 20) are: 12, 15, 10, 18, 12, 14, 16,

1

2. Calculate the mean, median, and mode of this data.

Solution: Mean: Sum of scores: 12 + 15 + 10 + 18 + 12 + 14 + 16 + 12 = 109 Number of scores: 8 Mean = 109 / 8 = 13.625 Median: Arrange the scores in ascending order: 10, 12, 12, 12, 14, 15, 16, 18 Since there are 8 scores (an even number), the median is the average of the 4th and 5th scores. Median = (12 + 14) / 2 = 13 Mode: The score 12 appears most frequently (3 times). Mode = 12 2.3 Probability Probability is the measure of the likelihood that an event will occur. It is expressed as a fraction, decimal, or percentage.

Formula:* Probability of an event = (Number of favorable outcomes) / (Total number of possible outcomes)

Example 4: Probability A bag contains 5 red balls, 3 blue balls, and 2 green balls. If a ball is drawn at random from the bag, what is the probability of drawing a red ball?

Solution: Number of favorable outcomes (red balls): 5 Total number of possible outcomes (total number of balls): 5 + 3 + 2 = 10 Probability of drawing a red ball: 5/10 = 1/2 = 0.5 = 50% Guided Practice (With Solutions)

Question 1: A survey was conducted in a Grade 7 class to determine their favourite South African sport.

The results are as follows: Rugby (12), Soccer (18), Cricket (6), Netball (4). Draw a bar graph to represent this data.

Solution: Axes: Horizontal axis: Sport (Rugby, Soccer, Cricket, Netball).

Vertical axis: Number of Students (Scale: 1 unit = 1 student).

Bars: Draw bars for each sport with heights corresponding to the number of students. Ensure all bars are of equal width.

Labelling: Label each axis and each bar clearly.