Let's Learn Mathematics

Types of Data

Introduction

Data refers to raw facts and figures collected during investigations or observations. Before we can analyze data, we need to understand what type of data we're working with.

In this lesson, we'll learn to identify different types of data including numerical, categorical, grouped and ungrouped data. Understanding these classifications helps us choose the right methods for organizing and analyzing our data.

Numeric Data

What is Numeric Data?

Numeric data consists of numbers that can be measured or counted. This type of data can be further divided into two main categories:

Discrete Data

Countable numbers with distinct, separate values:

  • The number of Nissan cars sold by Japan Motors, Ghana in a year
  • The number of children in a family
  • The number of learners in B8 class

Key Point: Discrete data can only take certain values (usually whole numbers).

Continuous Data

Measured numbers that can take any value within a range:

  • The weights of babies in a crèche (e.g. 4.5kg)
  • Heights of students
  • Temperature readings

Key Point: Continuous data can take any value (including fractions/decimals) within a range.

Group Discussion Activity

Task: In small groups, discuss and list 5 more examples of numeric data that could be collected during investigations. Identify each as discrete or continuous.

Example:

  • Discrete: Number of cars passing a toll booth each hour
  • Continuous: Time taken to complete a race (in seconds)

Non-Numeric (Categorical) Data

What is Categorical Data?

Categorical data consists of characteristics or attributes that can't be measured numerically. This type of data describes qualities or categories.

Examples of Categorical Data

  • Sex (male or female)
  • Income group (low, middle, high)
  • Movie type (action, comedy, drama)
  • Age group (child, teen, adult)
  • Marital status (single, married, divorced)
  • Boxers' weight class (featherweight, lightweight, etc.)

Ordinal Data

Categories with a meaningful order or ranking:

  • Boxers' weight class (ordered from light to heavy)
  • Age group (child, teen, adult)
  • Education level (primary, secondary, tertiary)

Key Point: The order matters in ordinal data, but the intervals between categories may not be equal.

Nominal Data

Categories without any inherent order:

  • Sex (male or female)
  • Marital status
  • Movie genres

Key Point: Nominal data has no numerical or ordered relationship between categories.

Group Discussion Activity

Task: In small groups, sort the following non-numeric data into ordinal and nominal categories:

Eye color, T-shirt size (S, M, L), Car brands, Restaurant ratings (1-5 stars), Blood type

Ordinal: T-shirt size, Restaurant ratings

Nominal: Eye color, Car brands, Blood type

Grouped vs Ungrouped Data

Understanding the Difference

Data can also be classified based on how it's organized - either as individual values or grouped into categories/ranges.

Ungrouped Data

Individual, raw data points not organized into groups:

Example: The scores for 11 learners in a class test:

25, 30, 35, 40, 45, 26, 29, 50, 45, 37, 47

Key Point: Each individual value is visible in ungrouped data.

Grouped Data

Data organized into categories or ranges:

Example: The same test scores grouped into ranges:

  • 25-35: 5 learners (25, 30, 26, 29, 35)
  • 36-50: 6 learners (40, 45, 50, 45, 37, 47)

Key Point: Grouped data shows how many values fall within each range, but hides individual values.

Practice Exercise

Task: The ages of 15 students are: 12, 13, 14, 12, 15, 13, 14, 16, 12, 13, 15, 14, 13, 12, 15

Group this data into the ranges 12-13 and 14-16 and count how many students fall into each group.

12-13: 8 students (12, 13, 12, 13, 12, 13, 13, 12)

14-16: 7 students (14, 14, 15, 16, 15, 14, 15)

Practice Exercise

Question 1

Classify each of the following as numeric (discrete/continuous) or categorical (ordinal/nominal) data:

  1. Number of books in a library
  2. Types of vehicles in a parking lot
  3. Temperature readings throughout the day
  4. Customer satisfaction ratings (Very satisfied, Satisfied, Neutral, Dissatisfied)

a. Numeric (discrete) - Countable whole numbers

b. Categorical (nominal) - No inherent order

c. Numeric (continuous) - Can take any value in a range

d. Categorical (ordinal) - Ordered categories

Question 2

The following are weights (in kg) of 20 students: 45, 52, 48, 55, 50, 49, 53, 51, 47, 54, 46, 52, 50, 49, 51, 53, 48, 50, 52, 49

Group this data into intervals of 45-49, 50-54 and state the frequency for each group.

45-49 kg: 6 students (45, 48, 49, 47, 46, 48, 49)

50-54 kg: 14 students (52, 55, 50, 53, 51, 54, 52, 50, 51, 53, 50, 52, 49)

Question 3

For each scenario, identify whether the data would be:

  1. Numeric or categorical
  2. If numeric, discrete or continuous
  3. If categorical, ordinal or nominal

Scenarios:

  1. A survey asking for people's favorite color
  2. Recording the time it takes runners to complete a race
  3. Counting the number of defective products in a factory each day
  4. A questionnaire about pain level (None, Mild, Moderate, Severe)

a. Categorical (nominal) - Colors have no order

b. Numeric (continuous) - Time can be measured precisely

c. Numeric (discrete) - Count of defective items

d. Categorical (ordinal) - Ordered pain levels

Ready for more challenges?

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