SHS1 Additional Mathematics · Semester 2 Week 13: Organising, Representing and Interpreting Data

Lesson notes

Learning Objectives

Indicator: 1.4.1.LI.2 - Categorise data and determine which scale of measurement describes the data.

By the end of the lesson, learners can:

Distinguish between quantitative and qualitative data and correctly classify given examples of each type.
Categorise qualitative data as nominal or ordinal and justify their categorisation by referring to the presence or absence of a natural order.
Categorise quantitative data as interval or ratio by testing for the presence of a true (absolute) zero.
Determine the appropriate scale of measurement for a given data set and explain their reasoning in simple language.
Evaluate a real-life data scenario, recommend the correct measurement scale, and defend their choice using the defining features of the scale.

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Curriculum details

Strand: Handling Data (Strand 4)
Sub-strand: Organising, Representing and Interpreting Data (4.1)
Content standard: 1.4.1.CS.1 - Investigate techniques for collecting data and determine measures of central tendency and dispersion. 1.4.1.LO.1 Collect quantitative and qualitative data, and organise and present data using graphs. 1.4.1.LO.2 Calculate the measures of central tendencies, and measures of dispersion and use simple language to interpret the results.
Indicator: 1.4.1.LI.2 - Categorise data and determine which scale of measurement describes the data.
Suggested placement: Semester 2, Week 13 (Week 33 of the year)
Our suggestion, laid out in curriculum order across three terms of twelve weeks. NaCCA does not fix the week, so follow your school's scheme of learning.
Curriculum reference: NaCCA curriculum document, p. 217

Exemplars (from the NaCCA curriculum)

Project-Based Learning, Think-pair-share, Group discussions, Talk for Learning
Learning Experience: Learners in groups categorise data and determine the appropriate scales of measurement for describing the data.
Activity 1:
- Learners in groups discuss the types of data, that is, quantitative and qualitative data and share their findings with the class
- Learners in groups explain quantitative data and qualitative data.
- Learners in groups state examples of quantitative and qualitative data.
Example of qualitative data: Interview data gathered from aspiring prefects in school, gender of a student, a person's nationality, colour preference, etc.
Examples of quantitative data: Test scores, age of students, time for completing a race, number of students reading various courses in school, etc.
Activity 3:
- Learners' groups discuss special features of qualitative and quantitative data in order to categorise them under nominal, ordinal, interval and ratio.
- Through brainstorming and discussion, as well as building on what others say, learners in groups discover that qualitative data can be further classified under nominal and ordinal and give examples
- Learners discover that nominal scale is used to classify data without any order or quantitative value.
Examples of nominal scale: Gender (Male, Female), Position on a ballot for an election, ethnic group, etc.
- Learners discover that ordinal scale is used to classify data with an order; that is, it shows a sequence.
Example of ordinal scale: Grades in exams (A1, B2, B3,...), Level of Education (Primary, JHS, SHS), Level of happiness (Very happy, Not happy, A little happy).
- Through brainstorming and discussion, as well as Building on what others say, learners in groups discover that quantitative data can be further classified under interval and ratio scales and statespecific examples of each.
- Learners in groups discover that the interval scale involves order and difference between variables, and their values can be added or subtracted, though it does not have a true zero.
Examples of Interval scales: Temperature, and test scores.
- Learners in their groups discover that the ratio scale involves the order of variables and the differences between them, and they have absolute zero but can't have a negative value.
Examples of Ratio scales: are height of an object, weight, age, etc.
Teaching and Learning Resources:
- SHS curriculum
- Research journals
- Internet or e-books
- Real-life examples
- Software (Excel, SPSS)
Assessment (1.4.1.AS.2). The document marks these depth-of-knowledge levels for this indicator: Level 3 Strategic reasoning.