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Statistics and Probability - Statistical Diagrams (Bar Charts, Pie Charts, Histograms)

Grade 8IGCSE

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

Angle of Sector=FrequencyTotal Frequency×360\text{Angle of Sector} = \frac{\text{Frequency}}{\text{Total Frequency}} \times 360^\circ

Percentage of Sector=FrequencyTotal Frequency×100%\text{Percentage of Sector} = \frac{\text{Frequency}}{\text{Total Frequency}} \times 100\%

Frequency Density=FrequencyClass Width\text{Frequency Density} = \frac{\text{Frequency}}{\text{Class Width}} (Used for advanced histograms)

Total Frequency=f\text{Total Frequency} = \sum f

💡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.