Using Histograms and Polygons
| Grade | Work Samples | |
|---|---|---|
| Midway through Stage 5 (end of Year 9) | End of Stage 5 (end of Year 10) | |
| Grade B | Haley | |
| Grade C | Eden Sascha Stacey | Kendall(C6) Bailey(C6) Cameron(C5) Indra(C5) |
| Grade D | Chandra Tai Ariel | Shane(D4) Jordan(D4) Lou(D4) Chris(D4) Ashley(D4) Riley(D3) Sam(D3) Kim(D3) Taylor(D3) |
| Grade E | Rania(E2) | |
- New Work Samples
- Drew
Description of activity
Students construct a cumulative frequency histogram and polygon (ogive) and use the ogive to find the median of the distribution. They then construct a frequency histogram and draw conclusions regarding the shape of the distribution, connecting the mean and median to the skewness of the distribution.
Suggested materials
Worksheet, calculator, ruler and pens/pencils
Context
Students have constructed frequency tables, frequency histograms, cumulative frequency histograms and ogives. They have discussed the meaning of skewness and how to recognise a skewed distribution. Students have also discussed the relationship between a skewed distribution and the mean and median.
Areas for Assessment
- Working mathematically
Knowledge, skills and understanding developed through inquiry, application of problem-solving strategies, communication, reasoning and reflection - Data
Knowledge, skills and understanding in collecting, representing, analysing and evaluating information
Outcomes
Data Representation (DS4.1)
Constructs, reads and interprets graphs, tables, charts and statistical information
Data Representation and Analysis (DS5.1.1)
Groups data to aid analysis and constructs frequency and cumulative frequency tables and graphs
Data Analysis and Evaluation (DS5.2.1)
Uses the interquartile range and standard deviation to analyse data
Questioning (WMS5.1.1)
Asks questions that could be explored using mathematics in relation to Stage 5.1 content
Applying Strategies (WMS5.1.2)
Analyses a mathematical or real-life situation, systematically applying problem-solving strategies
Communicating (WMS5.1.3)
Uses mathematical terminology and notation, algebraic symbols, diagrams, text and tables to explain mathematical ideas
Reasoning (WMS5.1.4)
Explains and verifies mathematical relationships
Reflecting (WMS5.1.5)
Links mathematical ideas and makes connections with, and generalisations about, existing knowledge and understanding in relation to Stage 5.1 content
Criteria for assessing learning
(These criteria would normally be communicated to students with the activity.)
Students will be assessed on their ability to:
- construct frequency histograms, cumulative frequency histograms and ogives
- use ogives to find the median
- explain skewness and how a skewed distribution influences the median and mean.