Students investigate an online multivariate data set, pose questions of interest relating to gender, education, employment and income, and present their findings as graphs (created on Excel).

- pose investigative questions
- interpret and use spreadsheets that display data
- analyse a data sample
- present displays
- discuss features of a data display

This is an open unit allowing students to investigate aspects of data that are of particular interest to them.

Students are building on the ideas from level 3. This includes posing comparison and relationship investigative questions, (collecting and) displaying measurement data, and comparing distributions visually.

Comparison investigative questions need to be about the group of interest and have an aggregate focus. For example: Do men with a (university) degree tend to earn more than men with school qualifications? Is there a relationship between level of education and income?

Students should determine the appropriate variables from within the given data and understand the principles of sample size.

Choosing a statistical sample is the act of deciding the size or number of observations that enable inferences to be made about a population from a sample. Students should understand that larger sample sizes generally lead to increased precision when estimating.

Students should use tables, dot plots and scatter plots to display data. They can compare (approximate) centres and the variation of the data. To use a scatter graphs students need to understand the relationship between the horizontal and vertical axes, i.e. x-axis and y-axis, and how one mark on the graph displays two variables.

When using a scatterplot a student should be looking at features such as the trend of the data points and how close the points are to the trend.

To accompany each display a student should write a statistically sound statement which refers to evidence in their display. “I notice...” can be a useful way for students to begin a statement. Students should recognise the limitations of their sample, and be be encouraged to write “I wonder...” statements for further investigation.

**Background **

What does the gender pay gap look like in New Zealand?

In the June 2015 quarter, median hourly pay for males was $24.07 and for females it was $21.23. The gender pay gap was 11.8 percent. This means that a typical male earned about 12 percent more for an hour’s work than a typical female.

Is the “glass ceiling” beginning to crack?

Graphing materials (either Excel or similar or graph paper etc.)

- Distribute or display copymaster 1. Have students discuss what it is suggesting.

Ask what information they think they’ll need to investigate this issue.

Together list possible variables.

- Make the household savings survey spreadsheet available and give students time to become familiar with the data categories.

Information about this dataset is available here.

- Brainstorm as a class a list of questions that can be investigated: For example:
- Do men with a (university) degree tend to earn more than men with school qualifications only?
- Do men with a (university) degree tend to earn more than women with a degree?
- Is there a relationship between level of education and income?
- Is there a relationship between income and gender?
- Are women with no qualifications more likely to be unemployed than men with no qualifications?

- Have student pairs choose a question from the list, or pose their own comparative question to investigate. More than one pair may choose to investigate the same question and their findings are likely to make for an interesting discussion.

Student pairs should identify which variables of the data set they will use, and be able to describe to the group how they plan to proceed with their investigation.

- 300 data items comprise the given data set.

It is important that students take a random sample (a discussion of why it would be a bad idea to choose from the dataset would be useful). The dataset is in random order so this can be done easily by taking (for example) the last 10 males, or every third person.

Students should be encouraged to focus the answer to their question on what these data show. They should be encouraged to avoid sweeping generalisations about the whole population but to justify their findings for the sample on the basis of the evidence they present.

The table below shows one way of presenting data to support the answer to the question: Do more women have higher qualifications than men? It is not the only, or necessarily the best, way of presenting the data.**Female****Male****Qualification****Frequency****Percent****Frequency****Percent****None**42 27.45 46 31.29 **School**62 40.52 51 34.69 **Vocational**30 19.61 36 24.49 **Degree**19 12.42 14 9.52

A scatter plot may be used to answer a questions such as: Is there a relationship between level of education and income?

- Have students present their data and their findings with reference to their chosen question. Have them explain their sampling process and their choice of data display. Ask each pair to explain any limitations of their findings/conclusions.

- As a class discuss the possible implications of their findings for their own education and job aspirations.

Dear Parents and Whānau,

This week in maths we have been investigating NZ statistics related to gender, education, employment and income.

Ask your child what key messages they have learned from this investigation and discuss their own plans for education and employment. Perhaps you may also want to discuss the way in which your education has impacted on your own employment situation.

Thank you.