SHS1 Additional Mathematics · Semester 2 Week 14: Organising, Representing and Interpreting Data

Lesson notes

Learning Objectives

Indicator: 1.4.1.LI.3 - Organise data into appropriate frequency distribution tables manually, and with Microsoft Excel.

By the end of the lesson, learners can:

Distinguish between ungrouped (raw) data and grouped data, and explain when grouping is appropriate.
Construct a frequency distribution table for ungrouped data manually, using tally marks, and verify that the frequencies sum to the total number of observations.
Construct a frequency distribution table for grouped data manually, determining appropriate class intervals, class limits, class boundaries, class midpoints, and class width.
Use Microsoft Excel to generate a frequency distribution table from raw data, using tools such as sorting and the COUNTIF function.
Interpret a frequency distribution table by reading frequencies, identifying the modal class (for grouped data) or modal value (for ungrouped data), and stating what the table reveals about the data.

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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.3 - Organise data into appropriate frequency distribution tables manually, and with Microsoft Excel.
Suggested placement: Semester 2, Week 14 (Week 34 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:

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Curriculum reference: NaCCA curriculum document, p. 219

Exemplars (from the NaCCA curriculum)

Group discussions, Talk for Learning and experiential learning.
Learning Experience: Learners in mixed-ability groups discuss grouped and ungrouped and how to organise data by hand and/or with the use of Excel spreadsheet.
Activity 1:
- Learners review ungrouped (raw) data and organise it using frequency tables
- Learners in their groups discover that ungrouped data is the data you gather from an experiment that is not sorted into categories or classified.
Example 1: The ages of some randomly selected football players are as follows 24,23,25,23,30,24,37,25,23, 22,25,22,31,29, 22,25,21,25,24,24,22 1. Make a frequency table for the data. 2. Represent this information on a graph or chart.
Solution:
- Frequency Table Age Tally Frequency 21 / 1 22 //// 4 23 /// 3 24 /// 3 25 //// 5 29 / 1 30 / 1 31 / 1 37 / 1 Total 20
- Learners in their groups discuss the importance of organising data into a frequency table.
- Learners in their groups solve a practical question and share their findings with the class.
Activity 2:
- Learners in their groups discuss grouped data.
- Learners in their groups discover that grouped data is data that has been bundled together in categories; that is, when given a large data, it is better to group them using intervals.
Example of interval for grouped data: 1-9, 10-19, 20-29 etc.
- Learners discover through interaction that the groups into which the entries are put are referred to as classes.
Example 2: 1-9, 10-19 and 20-29 are the classes.
- Learners in their groups discuss class limits, that is, lower- and upper-class limits.
Example 3: Taking 1-9 as the class, 1 represents the lower-class limit, and 9 represents the upper-class limit.
- Learners discover that the formula used to calculate class boundaries is given as ! (𝑢 𝑙 𝑜 𝑜 𝑐 + 𝑙 𝑙 𝑜 𝑡ℎ𝑒 𝑛 𝑐), is. )
Example 4:
- Learners in their groups apply their knowledge in finding midpoints to find the class midpoint, which is the average between the lower- and the upper-class limits.
- Learners in their groups discuss class width/size. Learners discover that class width/size is the difference between the upper- and lower-class boundaries of a class.
Teaching and Learning Resources:
- SHS curriculum
- Research journals
- Internet or e-books
- Real-life examples
- Software (Excel, SPSS)
Assessment (1.4.1.AS.3). The document marks these depth-of-knowledge levels for this indicator: Level 2 Skills of conceptual understanding.