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Statistics and Probability - Data Collection and Classification

Grade 8IGCSE

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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Qualitative Data: Non-numerical data that describes qualities or characteristics (e.g., hair color, favorite food).

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Quantitative Data: Numerical data that can be measured or counted.

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Discrete Data: Quantitative data that can only take specific values, often integers (e.g., number of children, shoe size).

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Continuous Data: Quantitative data that can take any value within a range, usually measured (e.g., height, weight, time).

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Primary Data: Data collected first-hand by the researcher for a specific purpose (e.g., surveys, experiments).

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Secondary Data: Data that has already been collected by someone else (e.g., internet, census records, newspapers).

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Population vs Sample: A population is the entire group being studied; a sample is a smaller group selected to represent the population.

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Bias: Systematic error introduced into sampling or testing by selecting or encouraging one outcome or answer over others.

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Grouped Data: Data organized into classes or intervals to make it easier to handle large sets of information.

📐Formulae

Relative Frequency=Frequency of an eventTotal Frequency\text{Relative Frequency} = \frac{\text{Frequency of an event}}{\text{Total Frequency}}

Class Midpoint=Lower Class Limit+Upper Class Limit2\text{Class Midpoint} = \frac{\text{Lower Class Limit} + \text{Upper Class Limit}}{2}

Range=Highest Value−Lowest Value\text{Range} = \text{Highest Value} - \text{Lowest Value}

Total Frequency (n)=∑f\text{Total Frequency (n)} = \sum f

💡Examples

Problem 1:

Classify the following types of data: (a) The number of goals scored in a football match, (b) The weight of apples in a basket, (c) The brand of mobile phones used by students.

Solution:

(a) Quantitative - Discrete; (b) Quantitative - Continuous; (c) Qualitative.

Explanation:

Goals are counted in whole numbers (Discrete). Weight is measured and can have any value like 1.25kg (Continuous). Mobile brands are categories, not numbers (Qualitative).

Problem 2:

A researcher wants to know the average height of 14-year-olds in a city of 50,000 people. They measure 100 students from one local basketball team. Identify the sample and explain if it is biased.

Solution:

Sample: The 100 students from the basketball team. It is biased.

Explanation:

The sample is biased because basketball players are likely to be taller than the average 14-year-old, meaning they do not represent the entire population accurately.

Problem 3:

A frequency table has a class interval for 'Time (t)' as 20≤t<3020 \le t < 30. Find the midpoint of this class and the class width.

Solution:

Midpoint = 25; Class Width = 10.

Explanation:

The midpoint is calculated as (20+30)/2=25(20 + 30) / 2 = 25. The class width is the difference between the upper and lower boundaries: 30−20=1030 - 20 = 10.