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Statistics - Classifying Statistical Data

Grade 9IGCSE

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

🔑Concepts

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Statistical data is broadly divided into two categories: Qualitative and Quantitative.

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Qualitative Data (Categorical): Data that describes non-numerical qualities or characteristics. Examples include colors, names, or types of animals.

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Quantitative Data (Numerical): Data that can be measured or counted and expressed as a number.

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Discrete Data: A type of quantitative data that can only take specific, distinct values (usually integers). It is often the result of counting. For example, the number of children in a family, n=3n = 3, or the number of cars in a parking lot.

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Continuous Data: A type of quantitative data that can take any value within a given range. It is often the result of measurement. For example, height h=165.5h = 165.5 cm, weight w=60.2w = 60.2 kg, or time t=12.45t = 12.45 s.

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Primary Data: Data collected first-hand by the researcher for a specific purpose.

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Secondary Data: Data that has already been collected by someone else (e.g., from the internet, books, or government records).

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Grouped Data: When dealing with large sets of continuous data, it is organized into class intervals, such as 10<x≤2010 < x \le 20.

📐Formulae

Midpoint of a Class Interval=Lower Boundary+Upper Boundary2\text{Midpoint of a Class Interval} = \frac{\text{Lower Boundary} + \text{Upper Boundary}}{2}

Class Width=Upper Boundary−Lower Boundary\text{Class Width} = \text{Upper Boundary} - \text{Lower Boundary}

Frequency Density=FrequencyClass Width\text{Frequency Density} = \frac{\text{Frequency}}{\text{Class Width}}

💡Examples

Problem 1:

Classify the following types of data as either Discrete or Continuous:

  1. The number of students in a classroom.
  2. The time taken to run 100100 meters.
  3. The number of goals scored in a football match.
  4. The mass of an apple.

Solution:

  1. Discrete (you cannot have 25.525.5 students).
  2. Continuous (time can be measured to any degree of accuracy, e.g., 13.2413.24 seconds).
  3. Discrete (goals are counted in whole numbers).
  4. Continuous (mass is measured, e.g., 150.5150.5 grams).

Explanation:

Discrete data involves counting objects or events, while continuous data involves measurements that can fall anywhere on a scale.

Problem 2:

A researcher is studying the heights of plants. The heights (hh) in cm are recorded as follows: 12.112.1, 15.415.4, 18.918.9, 11.211.2, and 14.514.5. Suggest a suitable grouped frequency table structure using a class width of 55 starting from 1010.

Solution:

The class intervals would be: 10≤h<1510 \le h < 15 15≤h<2015 \le h < 20

Explanation:

Since height is continuous data, we use inequalities to define the boundaries. A class width of 55 means the intervals span 55 units (e.g., 15−10=515 - 10 = 5).

Problem 3:

Calculate the midpoint of the class interval 20<x≤3020 < x \le 30.

Solution:

Midpoint=20+302\text{Midpoint} = \frac{20 + 30}{2} Midpoint=502\text{Midpoint} = \frac{50}{2} Midpoint=25\text{Midpoint} = 25

Explanation:

The midpoint is the average of the lower and upper boundaries of the class interval.