Review the key concepts, formulae, and examples before starting your quiz.
🔑Concepts
Data Types: Understanding the difference between Discrete data (counted, e.g., number of children) and Continuous data (measured, e.g., height, time).
Bar Charts: Used for discrete or categorical data. Bars must have equal width and equal gaps between them. The height represents the frequency.
Pie Charts: Circular diagrams where each sector represents a proportion of the whole. The total of all sector angles must equal 360°.
Histograms: Used for continuous data. Unlike bar charts, there are no gaps between the bars. The area (or height in basic Grade 8 versions) represents frequency.
Frequency Tables: A method of organizing raw data using tally marks to summarize the frequency of each category or class interval.
Class Intervals: In histograms, data is often grouped into ranges (e.g., 0 ≤ x < 10). The 'Class Width' is the difference between the upper and lower boundaries.
📐Formulae
(Used for advanced histograms)
💡Examples
Problem 1:
A survey of 60 students asked for their favorite color. 15 students chose 'Blue'. Calculate the angle this sector would occupy on a pie chart.
Solution:
Angle = (15 / 60) * 360° = 0.25 * 360° = 90°
Explanation:
To find the angle, divide the specific frequency by the total frequency to find the fraction of the circle, then multiply by 360 degrees.
Problem 2:
In a histogram representing the heights of plants, the class interval '10 < h ≤ 20' has a frequency of 8 and the class interval '20 < h ≤ 30' has a frequency of 12. What is the total number of plants measured in these two intervals?
Solution:
Total = 8 + 12 = 20 plants
Explanation:
In a basic histogram where class widths are equal, the frequency is simply the height of the bars. Adding the frequencies of the required intervals gives the total count.
Problem 3:
A bar chart shows that 5 people have 0 pets, 8 people have 1 pet, and 2 people have 2 pets. Calculate the total number of pets owned by this group.
Solution:
Total Pets = (5 * 0) + (8 * 1) + (2 * 2) = 0 + 8 + 4 = 12 pets
Explanation:
To find the total quantity from a frequency distribution, multiply each value (number of pets) by its frequency (number of people) and sum the results.