Curriculum links
Mathematics curriculum links: (mathematics in the New Zealand curriculum 1992)
Level 7
- Collect data, present it visually, and discuss prominent features of the data.
- Calculate sample statistics, including mean and standard deviation and verify these by reference to a data distribution.
National Ethnic Population Projections in New Zealand
In this edition we are focusing on New Zealand’s age demographic by ethnic group as it appears in 2006 and how it is projected to appear in 2026. In particular, the activities and questions support internally assessed Unit Standard 12332 – Demonstrate knowledge of measures and displays used to compare data sets.
In this activity, students are asked to consider the back-to-back age population pyramids for four New Zealand ethnic groups in 2006 and in 2026. Students will identify key features of the data and in particular compare and contrast the 2006 and 2026 age demographics with reference to measures of centre and measures of spread. Later they will be asked to consider the 2006 data solely, allowing for comparison across the four ethnic groups: European and Other, Mäori, Pacific and Asian.
An underlying goal of this activity is to establish students’ understanding of the link between a histogram and a box and whisker plot. Students will learn how to approximate key statistics from the population pyramids in order to draw approximate box and whisker plots. Specifically, they will be asked to comment on features that histograms and box and whisker plots have in common and the important information that has been lost along the way.
The web activity works to further this understanding. Students are required to select their own groups for comparison of weekly income. They will compare data sets by drawing histograms and box and whisker plots and commenting on notable features of the distributions as they appear in the displays. They will also calculate measures of centre and spread to write a detailed comparison of the data sets. It is expected students will already be familiar with the following ideas: mean, median, range, minimum, maximum, lower quartile, upper quartile, interquartile range, standard deviation.
Did you know?
Over the next two decades:
- New Zealand's Mäori, Asian and Pacific populations are projected to grow.
- The 'European or Other (including New Zealander)', Mäori, Asian and Pacific populations are projected to age, which is reflected in rising median ages and increasing proportions of people in the older ages.
Teacher’s tips and solutions
PART ONE: Making sense of the information
- European or Other as shown by the higher scale on the horizontal axis compared with the other ethnicities.
- Approximately 18,000
- Approximately 50,000
- The population pyramids in 2026 for these ethnic groups overall are thicker than in 2006.
- The wider base of the pyramid tapering at the higher ages.
- All four graphs are thicker at the top (over 65) end of the pyramid in 2026 than in 2006.
- Draw a horizontal line through each side of the pyramid at the point where it appears that half the shading is above
the line and half is below the line.
- Immigration to New Zealand of young Asian adults at around age 21 especially for tertiary study. These people may decide to remain in New Zealand hence the spike in 20 year time at age 41. Example feature for comment: The relatively small proportion of Asian children in 2006 as shown by the dip towards the base of the pyramid. In comparison, the base of the 2026 pyramid is thicker and there is even a bump which forms the third highest peak on the distribution.
- Increased deaths and fewer women at child bearing age thus lowering the momentum for population growth. In 2026 the base of the pyramid is smaller as compared to 2006. More specifically in 2006, the number of newborn
children forms a small peak but in 2026 it appears to be part of a dip.
- This exercise is designed to encourage students to think critically about what the population pyramid’s shape means.
PART TWO: Mix and Match
Answers 1.1, 1.2
European or Other: B, G, J
Mäori: A, F, L
Asian: D, H, I
Pacific: C, E, K
Answer 2 and 3
Please note: It is intended that Part Two will provide the impetus for an in depth class
discussion and debate regarding the pros and cons of histograms versus box and whisker plots. The primary objective is for students to realise that specific detail displayed on a histogram such as troughs, spikes, holes, bumps, frequency and distribution shape are lost or less apparent on a box and whisker plot.
PART THREE: Drawing Comparisons
Some possible statements include:
- The Mäori and Pacific groups have a similar median age of about 22 years. The Asian median age looks to be about five years greater than this and the European or other median age is the greatest at about 38 years.
- The interquartile range of ages for the European or Other ethnic group looks to be about 40 years in comparison to the interquartile range of ages for the other three groups which all appear to be around 30 years.
- All groups range from 0 to 90+ years.
- The European or Other ethnic group plot is quite symmetrical with the median centred in the middle of the box and the whiskers of similar length. The other ethnic groups appear skewed right as the bulk of their population are aged less than about 40 years of age.
- The European or Other median age is similar to the upper quartile age for the Pacific population. This shows that 75% of
the Pacific population fall into the same age bracket as 50% of the European or Other group.
- The box and whisker plot for Mäori and Pacific people are similar indicating the age distribution of Mäori and Pacific
people in New Zealand are comparable