Curriculum links
NCEA Mathematics Achievement Standard AS 90193
- Use statistical methods and information
Mathematics, Statistics Strand - Level 6
Background
This activity is designed to give students practice in answering a question. It also gives the opportunity for students to be critical of their work and to think more deeply about the question and how best to answer it. Was the question they answered the right question to solve the problem? Was the data they used suitable? The data on the Manawatu came from Table Builder. The links below are to instructions on how to find data about your own area (from Table Builder), how to use it to find just the data you want, and more information about area units.
Some possible answers
The answers below are a guide to possible responses to the questions about the conclusion. There are lots of different possible answers. It is how well the students justify the answers that is important.
The spreadsheet gives the calculations.
1. Use the graph and the calculations to:
(a) Answer your question.
Overall, the percentage of households with Internet access was higher in the city that in the country.
(b) State two pieces of evidence that support what you have said.
Overall, 40 percent of households in urban area units have Internet access, compared with 35 percent in rural area units.
The dot plot shows that the urban areas' percentages are further to the right than the rural area ones. This shows the higher levels of Internet access.
(c) Give one piece of evidence that contradicts what you have said.
Some places in the city (eg Awapuni North) have a lower rate of Internet access than some places in the country (eg Kairanga). The dots overlap on the dot plot.
(d) Discuss whether the evidence supports the opinions of Matt or Tina.
The evidence does not support either. While it is true that the rate of Internet access in the country is lower on average, in some country areas it is higher than in some city areas. Also, just because it is lower doesn’t mean that living in the country causes people to not have Internet access, which is what Matt is saying.
(e) Describe what extra information the display gives you.
Looking at the names of the area units helps to identify the pattern of low or high Internet usage. Local knowledge may help to see if there are reasons for an area's level of Internet access other than geographic placement.
2. Evaluate your answer by:
(a) Describing how well your data and analysis actually answered the question.
The data showed that in the Manawatu region Internet access is lower in the country. So it answered the question for that area. It may not be true for other areas, and it was not true for some parts of the city and some parts of the country.
(b) Stating other information might help you to explore the question more. (Think about other factors that might influence having Internet access.)
Other reasons for people having Internet access (or not) might be the cost of having to buy a computer as well as hook up. Some areas might not have access to the Internet because they have old phone lines. Some people just might not want it. Investigating the different area units and looking for this other information would be useful.
(c) Explaining what limitation of this data makes your answer less relevant to solving the problem.
The data is almost five years old now.
(d) Explaining why this is a problem.
In five years, there have been big changes in the cost of technology and in how easy it is to access the Internet.
(e) Describing one advantage of using this data to answer your question.
It comes from census data, so most people in the area would probably have answered the question. This means the data is more reliable.
3. The data is given using area units. (a) What is an advantage of looking at small areas rather than the overall totals?
You can look at the different areas in the data and use your knowledge about the district to understand the data.
(b) Look at which category the different areas are placed in. Were the area units correctly classified as urban or rural. For example, where should Feilding go?
Feilding is a large country town and could be classified as urban. But it is still a way away from the city and probably should stay in the rural category because of that. Aokautere is a rural area but is very close to Massey University and the city, so probably fits best in the urban category. It seems reasonable to put rural areas that are very close to the city in with the urban category, and those further away in with the rural, even if they are towns.