SHS3 Mathematics · Semester 2, Week 11

Statistical Reasoning and Its Application in Real Life

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Curriculum details

Strand: Making Sense of and Using Data (Strand 4)
Sub-strand: Statistical Reasoning and Its Application in Real Life (4.1)
Content standard: 3.4.1.CS.1 - Demonstrate understanding of data handling involving simple mathematical relationships of bivariate data in observational and experimental contexts. 3.4.1.LO.1 Establish simple mathematical relationships between two variables in a given observational or experimental context; illustrate using scatter graphs and use them to solve and/or pose problems.
Indicator: 3.4.1.LI.1 - Establish simple mathematical relationships between two variables in a given observational or experimental context; illustrate using scatter graphs and use them to solve and/or pose problems.
Suggested placement: Semester 2, Week 11 (Week 31 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.
Source document note: The official curriculum document has a fault in this entry, so the curriculum text above is transcribed exactly as printed:

exemplars - p.369: this exemplar sets a two-dimensional construct - a stacked fraction, an index or a column vector - which the text layer flattens into separate lines, so the parts are present but their vertical arrangement is lost; read the page
Curriculum reference: NaCCA curriculum document, p. 369

Exemplars (from the NaCCA curriculum)

Encourage learners to use technology Literacy Skills, combined problem-solving competency and critical thinking skills to collect data from an observational study in which, for example, the interest is the relationship between weight and height to establish mathematical relationships of bivariate data in observational and experimental context and use them to solve related problems.
Project-based Learning: In convenient groups, task learners to collect data of interest within or outside the school community (including using social media platforms or any technological means for collecting data). Provide opportunities for students to evaluate various real-world scenarios and make decisions based on the data at hand.
Examples of data collected are presented in the tables below.

Three paired-data tables: meat and price, litres and kilometres driven, and score and frequency. — Three small two-column tables side by side. The first pairs Meat in kilograms with Price: 1 and 14, 2 and 28, 3 and 32, 5 and 70. The second pairs Litres with Km Driven: 20 and 160, 30 and 240, 45 and 360, 50 and 400. The third pairs Score with Frequency: 10 and 2, 20 and 6, 35 and 4, 50 and 3.

 Meat Price Litres Km Score Frequency (kg) Driven i. 10 1 2 20 14 160 ii. 20 2 6 iii. 28 30 240 iv. 35 3 45 4 32 360 v. 5 50 50 3 70 400 i. Identify which table does not show bivariate data. ii. Identify the independent and dependent variables in the tables that show bivariate data. iii. What effect has the number of litres of fuel used on the number of kilometres driven? (Learners should note the relationship between the two variables.)
iv. Can any comparison be made between Score and Frequency in Table C? [Note in this case, though the frequencies are not the same, there is (i) one variable - univariate and (ii) no relationship between Score and Frequency.]
Example: The bivariate data presented in the table below shows the hours studied and the percentage scores of two variables--independent and dependent - respectively obtained in a statistics course by 10 learners.

Table of ten learners with hours studied and test scores, from Gifa 3 and 90 to Baaba 1 and 77. — A table with a pink header reading Learner, Hours Studied(h) and Test Score(s). The rows are Gifa 3 and 90, Kewo 1 and 86, Dauda 5 and 84, Ekow 4 and 92, Kapio 3 and 91, Alhassan 5 and 100, Serwaa 0 and 76, Ada 1 and 82, Fofio 2 and 85, and Baaba 1 and 77.

 Learner Hours Test Studied(h) Score(s) Gifa 3 90 Kewo 1 86 Dauda 5 84 Ekow 4 92 Kapio 3 91 Alhassan 5 100 Serwaa 0 76 Ada 1 82 Fofio 2 85 Baaba 1 77 i. Place the information on a graph sheet (scatter plot) by plotting each learner as an ordered pair with Hours Studied on the x-axis and Test Score on the y-axis. ii. Discuss the scatter plot, find the relationship between hours studied and test score, draw their conclusion and justify it. iii. Pose questions based on the analyses.
Teaching and Learning Resources:
- * Samples of bivariate data. * Computer application software such as MS Excel, MS Word, Wordpad, etc. * Mathematical sets. * Technology tools such as computers, mobile phones, etc. * Graph sheets * A computer with data-managment software like MS Excel, MS PowerPoint, etc., * A4 and A3 papers, manila cards, flip charts, markers, colour pens, etc.
Assessment (3.4.1.AS.1). The document marks these depth-of-knowledge levels for this indicator: Level 2 Skills of conceptual understanding; Level 3 Strategic reasoning.

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