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Secondary activities
Secondary StatZing! September 2004
Who lives in this area? Ko wai e noho ana i tenei rohe activity
Curriculum links
Mathematics level 5 Statistics:
Within a range of meaningful contexts, students should be able to discuss discrete and continuous numeric data presented in quality displays.
NCEA mathematics 1.5 (AS90193)
- Interpret statistical information and answer straightforward questions.
- Interpret statistical information and comment on a range of features
- Evaluate statistical information.
Background
The activity in StatZing! encourages students to apply number skills and use them to examine changing demographic patterns in geographical areas in New Zealand. Students can examine and compare data within areas, and calculate percentage increases/decreases and averages by analysing tables and statistical graphs.
The attached workbook at the bottom of the page contains the teacher sheet, student sheet and a sheet with data for all areas in New Zealand. You can adapt the activity in StatZing! to show the data for your own area.
The downloadable files are in Microsoft Excel 97 format(s) (551 KB).
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.
Extension questions
- Can you just add the percentage changes for 1991-1996 and 1996-2001, to get the percentage change for 1991-2001? If not why not?
- We've used differences and percentage changes to look at changes to the population over five-year periods. Which do you prefer? Or, discuss the advantages and disadvantages of each method.
- Take any count (not a percentage). For example, the count for Pinehaven in 2001 is 3,087. Use the adding-digits method to find if it has 3 as a factor:
- add the digits: 3 + 0 + 8 + 7 = 18
then add 18's digits: 1 + 8 = 9.
If this has 3 as a factor, then so does 3,087.
Promise a chocolate fish to anyone who finds a count that does not have 3 as a factor!
Point out that all census data is confidential and very small counts can reveal someone's private information. To preserve confidentiality about individuals, while still making information about groups available, census counts are 'random rounded' to a nearby number that has 3 as a factor.
If the counts all have 3 as a factor, what about the differences?
Suggested answers to the questions in StatZing!
- Trentham South, 1991–1996, an increase of 183.
- Emerald Hill, 1996–2001, an increase of 246.
- Nabhra, an increase of 48 percent. Answers will vary. One possible answer is - it is a new subdivision.
- Brentwood (117)
Elderslea (66)
Wallaceville (60)
Maidstone (9)
Upper Hutt Central (21)
Ebdentown (108)
Totara Park (165)
Clouston Park (117)
Maoribank (102)
Akatarawa (9)
Pinehaven (102)
Trentham South (279)
Answers will vary.
- Ideally, the graph would show the distribution of the percentage changes, and show where each area belongs. A bar graph is a start, and a bar graph sorted by change would be better. Better still would be a histogram. For this, you could round the changes to whole percentages first. A fine piece of data visualisation would be to do a histogram, and write the area names in the 'bricks' of the histogram. The distribution consists of an outlier at the bottom (Trentham South on -30.7 percent), a cluster of 15 areas from -6.7 percent to +2.4 percent, a tail of 4 areas then an outlier at the top (Nahbra on 48.4 percent). The centre of the distribution is just negative. It is desirable to translate all the above into statements about the city's context: Most of Upper Hutt's areas have counts for 2001 that are similar or slightly less than those for 1996. However, ..."
- The vertical line should mark the mean (or median) of the counts, and will therefore lie at the centre of the ends of the bars for 2001. The graph with the line shows that the mean area count is about 1700, and that the counts vary widely about this. You can read off which areas are close to the mean. A histogram, stem-and-leaf plot (with mean marked) or a boxplot would show these features too.
- Ideally, the graph would show the distribution of the counts, and show where each area belongs. A bar graph is a start, and a bar graph sorted by count would be better. Better still would be a histogram. For this, you might need to round the counts (to 100s perhaps) first. Again, a fine piece of data visualisation would be to do a histogram, and write the area names in the 'bricks' of the histogram. Also, you could use a stem-and-leaf plot. The distribution has two distinct clusters. The areas are probably defined according to geographical boundaries, apparently without an effort to keep the counts similar.
- (a)The population in Trentham South has gone up, then down, whereas Totara Park has been steadily declining.
(b) In certain areas of Upper Hutt the population has grown, BUT overall the population has declined over the 10 years.
(c) It has increased, BUT only 3.4 percent of the Upper Hutt population live there.
(d) The statistics shown do not indicate the ages of people living in the Upper Hutt region. A breakdown of the age distribution can be found in this table.
- Answers will vary. Possible answers could be:
A range of census-based data is available on the website for these areas. Examples are: counts of population by age and gender; counts of households by dwelling type and number of usual residents in household. A full list can be found in Table Finder
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