Males versus females teachers page

Secondary activities
Males versus females activity one
Males versus females activity two
The changing population activity

Curriculum links
Mathematics, Statistics Strand - Levels 5 to 8
Mathematics, Algebra Strand Levels 6 and 7

NCEA Mathematics Achievement Standard 1.2 (AS 90148)
NCEA Mathematics Achievement Standard 1.5 (AS 90913)
NCEA Mathematics Achievement Standard 3.5 (AS 90645)

Background
These activities have been prepared to encourage students to apply their number skills to examining changing demographic patterns in New Zealand. The investigation looks at:

• comparing counts across regions, genders and age groups
• percentage increases/decreases
• generating and analysing tables and statistical graphs.

The activities and the Excel workbook are intended to help teachers and students build skills in data exploration.

There are three activities for students to complete. For the Males versus females two activity, students will use Table Finder and Table Builder to find the data they need to complete the questions.

For the Males versus females one activity and The changing population activity, the data and graphs are in the Excel workbook attached at the bottom of the page.

Males versus females activity one answers

Answers will vary but should contain information similar to this definition.

1. Completed table is in the sheet 2001 data in the attached Excel workbook.
2. Graph is included in the sheet 2001 data in the attached Excel workbook.
   
   The equation is:
   Proportion of males = 1 - Proportion of females
   
3. The proportion of females is asymmetrical, with several regions close together near the maximum (0.516 at Nelson), and a tail down to 0.496 (West Coast). There is an outlier at 0.434 (Area outside region). As we'd expect, the proportion for New Zealand is at the centre (it is a mean weighted by size, in fact). Nelson is 0.004 above, and the West Coast is 0.016 below.
4. Graph is included in the sheet 2001 data in the attached Excel workbook. There's a very strong relationship. As there are more females in New Zealand than males, the points are mostly below the y = x line. Perhaps they are lower for larger regions. The Auckland region is out on its own in size.
5. Answers will vary. Here are some possible responses:

• The regions differ in employment and education options.
• They probably differ in age structure, and regions with more people in the older age groups are likely to have a higher proportion of females.

7. The counts are useful because they give the total size of each region. The proportions are useful, as they help us compare regions with size removed.
   

Males versus females activity two answers
The data the students will use to complete the tasks in this activity can be found in this Table Builder table. The data and graphs used in these answers can be found in the By age group sheet in the Excel workbook above.

1.

The proportion of females has increased. It may have been affected by age structure changes, migration and other factors.

2.

It seems that the proportion of females in 1991 and 1996 was similar to that for 2001, and even lower in earlier years.

3. Answers will vary. Some suggested responses:

• Males have higher counts at the low-age end, and females have higher counts at the high-age end.
• Both have a dip around 20-24 and 24-29, and a hill around 35-39. There will be a number of possible reasons.

4. The patterns here are likely to be the same as for New Zealand.
5. Answers will vary. Students could compare the area unit, town or rural area they live in with the New Zealand patterns.
6. Students could examine the graph to see whether the dips and crests of 1991 moved up a five-year age group or not with each census.

The Changing population activity answers

1. Completed table is in the Changes since 1996 sheet in the Excel workbook above.
2. Students could have produced a histogram or a stem-and-leaf or equivalent, with the regions named. The graph could use percent or number. It could be a table or bar graph sorted by number or percent.
   The distribution of percents shows:

• regions around -6 percent (West Coast and Southland)
• a cluster from about -4 percent to 3 percent
• two regions around 6 percent
• Tasman near 9 percent.
  The numbers show a somewhat different picture.

3. Answers will vary. Here is a possible response: the change as a number tells us something about the region, but the change as a percent gives the change as it relates to the size of the population in the region. The latter will be of more value to the people who live there.
4. The graph shows a very strong relationship, as we would expect, with some regions drifting up or down from the trend. If this drift is related to size, it would be seen more clearly by a graph of change against size in 1996. It does not seem to be related to size apart from the outlier (ie Auckland). Ten of the 16 points are above the y = x line. The regression line is dominated by the outlier (Auckland).

Table Finder
Quick guide to using Table Finder/Table Builder
Help notes for using Table Finder
Help notes for using Table Builder

Related links

The downloadable files are in Microsoft Excel 97 format(s). If you do not have access to Excel 97 or higher, you may use the Excel file viewer to view, print and export the contents of this file.
Regional data males vs females teacher version.xls