1.3 - Interpret/Apply Information

What Is 1.3 Interpret/Apply Information All About?

Mathematics 1.3

Achievement Standard 91946

Interpret and apply mathematical and statistical information in context

5 Credits

External

This assessment is about making informed judgements and decisions using information from media with mathematics and statistics in it.

The following page covers each of these skills and how to sit the assessment.

Assessment Format

This standard is assessed as an exam at the end of the year.

You may find that previous versions of this exam used a different format to this.

Students must be able to communicate what graphs, tables, and articles mean and make an informed judgement on whether the conclusions are correct or whether there are limitations.

The test involves reviewing graphs, tables, and articles presented in a real world context and writing about them.

The teacher cannot offer guidance and support during the assessment.

All work must be completed by the student during the assessment.

Skills for 1.3 Interpret/Apply Information

This standard requires students to:

interpret information and connect it to a real life context including:
- graphs and infographics
- tables
- articles or text
explain how an informed judgement or decision was reached using information
communicate the meaning of mathematical and statistical information to a non-specialist audience
explain variation in the extracted information
consider the assumptions and limitations
examine claims and consider if they are valid
identify misleading information

Statistics and Probability Skills

Students should be comfortable with the content taught in the junior school for Probability and Statistics.

More information is available on the Junior Statistics and Junior Probability pages.

Data Displays

Students should know how to interpret information from the many types of data displays.

Other displays may also be used in the final examination but these resources cover many of the common forms of data display students will likely see in the real world.

The following videos will explain each of the main data displays:

Types of Graphs and When To Use Them

Pie Chart

Scatter Plot

Box Plot

Histogram

Stacked Bar Chart

Area Chart

Time Series

Heat Map

Data In Tables

Students should know how to read and be able to answer questions about data contained in a table.

This includes common table types like Two Way Tables and Pivot Tables.

Reading and Interpreting Tables

What are Two Way Tables?

What is a Pivot Table?

Data Analysis Tools

Students should know how to analyse data using commonly used software such as Excel, Google Sheets, and NZ Grapher.

We will use these tools in class to make our own graphs and analyse them.

Going through the process of analysing your own data also helps with understanding data in tables and displays along with how to interpret them.

More information on using NZ Grapher can be found in the Page on the 1.1 Statistical Enquiry Standard.

Intro To Excel

Data Cleaning In Excel

Intro To Google Sheets

Intro To NZ Grapher

Data In Text or Articles

Students should know how to read and be able to answer questions about a piece of text which contains data.

This includes:

News Articles
Websites
Videos (TikToks, Reels, YouTube Videos)

These videos may help with working on this skill.

Interpreting Data In A Written Text

Understanding Graphs When They Are Used In Real Life

Spotting Misleading Statistics In The News

Understanding What's Going On In This Graph

Communicating Clearly

Students should be able to communicate the meaning of mathematical and statistical information to a non-specialist audience.

Here is a video which explains how to communicate using a variety of mathematical representations.

Sources Of Variation

Students should be able to explain variation in the extracted information.

Sources of variation include:

Natural or Real
Occasion-to-Occasion
Measurement
Induced
Sampling

Sometimes you'll read the term Non-Sampling Variation. This is all variation except for Sampling Variation. This video here explains this.

The following are explanations for each form of variation.

Natural or Real Variation

Variation that occurs because individuals are different.

This is the kind of variation we expect to measure. For some measures this will be large while others will be small.

e.g. different people will have different heights, different weights, etc. Basketball players will have less Natural Variation in height than the general population.

Occasion-to-Occasion Variation

Happens because some variables are not consistent, even over short time periods. Well designed experiments reduce this by taking recordings at the same time or in the same situations.

E.g.

Blood pressure is different even 5 minutes after it's recorded. Test results are affected by the time of day the test is sat.

Measurement Variation

Happens because no measurement or person reading the measurement is perfect.

Well designed experiments reduce this by using accurate measuring equipment along with being careful and thorough during the recording. Good experiments quote the error range associated with any reading.

e.g. If a ruler is used, the smallest measurement that can be done is 1mm. This means for any measurement, there will be an error of up to 0.5mm.

Induced Variation

Happens by members of the population being in different circumstances.

Well designed experiments will try and reduce the differences between groups.

This is often done with a control group - a separate group that do not have the new procedure or circumstances.

e.g. using students from the same year level or skill level.

Sampling Variation

Happens because random chance causes people in groups to be a little different. The smaller the sample, the more likely there will be an extreme difference. Taking larger samples reduces this error but this is costly and is never truly removed. That is why we use confidence internals which measure the likely sample error.

e.g. one random group of students might do better in a test than another random group of students.

Assumptions and Limitations

Students should be able to consider the assumptions and limitations of evidence presented to them.

Watch these videos to understand this better.

Assumptions

Strengths and Limitations

Judgements and Decisions

Students should be able to explain how a judgement or decision was reached using information provided to them.

This videos explains one example of this in probability calculations.

Fact Checking

Students should be able to examine claims and consider if they are valid.

Take a look at these sites for more info on how to misinformation and disinformation are spread and how to fact check.

2022 Misinformation and Disinformation Study

Misinformation, Disinformation, and How To Protect Yourself

How To Spot A Misleading Graph

Our Process - FactCheck.orgAt FactCheck.org, we follow a process when we select, research, write, edit and, if necessary, correct our articles. Topics Our topics vary slightly depending on the election cycle. In all years, we closely monitor the factual accuracy of what is said by the president and top administration officials, as well as congressional and party leaders. However, we primarily focus on presidential candidates in presidential election years, and on the top Senate races in midterm elections.

Fake News

Students should be able to identify misleading information.

Take a look at this website for a bit of a hand in spotting fake news.

WILL YOU FALL FOR FAKE NEWS?Get the full story at Your News Bulletin.

Additional Resources for 1.3 Interpret/Apply Information

Ensure you have a strong knowledge of the Statistics and Probability parts of Junior Mathematics.

Liz Sneddon

Mrs Liz Sneddon, of Ormiston Senior College, has created a bunch of resources to assist with teaching of statistics, including support for the new 1.3 Standard.

Here is a video of her explaining the standard and a link to a handout.

Be aware that these resources were created in January of 2022 and so may not reflect the current assessment entirely.

NEW Achievement Standard Info Sheets AS1.3 Maths and Stats literacy.docx.pdf

Practice Assessments and Marking Schemes

The following are practice assessments along with their marking schemes.

91946-res-2024.pdf