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Under pressure? - teachers page

Secondary activity

Under pressure?

Curriculum links

Mathematics: Statistics strand – level 5

  • plan and conduct statistical investigations of variables associated with different categories within a data set, or variations of variables over time
  • find, and authenticate by reference to appropriate displays, data measures such as mean, median, mode, inter-quartile range, and range
  • discuss discrete and continuous numeric data presented in quality displays
  • collect and display comparative samples in appropriate displays such as back-to-back stem-and-leaf, box-and-whisker, and composite bar graphs.

 

Background

This activity Under pressure? asks students to investigate the problem of perceived prejudice against single people. Many organisations offer cut rates to couples, and there are often negative connotations to terms such as ‘spinster’. A discussion of some of these issues could be a good way to introduce the activity.

You may want to use a subset of the dataset where students are analysing the data manually.

The sample answers below are to show one way of answering the question and what sorts of comments are expected for justifications. It is not the only, or necessarily the best, way of doing the activity.

The problem-plan-data-analysis-conclusion (PPDAC) structure used in the activity fits with the draft new curriculum. Information on PPDAC can be found at the CensusAtSchool website:

www.censusatschool.org.nz/resources/how-kids-learn/

 

The sample answers below are based on the complete dataset. Students could also do graphs and make comments on the categorical variables.





Sample answers



Percentage of married and never married people in different age groups.



There are large numbers of people who have never married in the lower age groups. For people over 30 years, many more people are married.


Weekly Income by Marital Status.

It seems that married people have higher incomes than those who have never married (the highest income is from a never-married person, however). This might be because the non-married respondents are younger over all than the married ones. Young people tend to earn less. Apart from the outliers, there is a smaller range of income for people who have never been married.



Hours Worked per Week by Marital Status.



The hours worked are highly skewed, probably because lots of people work a standard 40-hour week. On average, the people who have never married seem to work shorter hours, but only by a very small amount. However, more of them seem to work part time. This group will include lots of under-20s who may still be studying.

Calculations


Married Never married
Age Hours Income Age Hours Income
Mean 35.94 35.86 607.79 25.17 30.56 520.36
Median 36.5 40 546 23 38 475
Upper quartile 40.75 45 807 29.25 40 720
Lower quartile 33 24 393 19.75 15 242.75
Maximum 45 70 1724 45 70 1789
Minimum 16 4 18 15 2 11
Range 29 66 1706 30 68 1778
















 

Conclusion


This will vary depending on the data analysed. It is important that the evidence stated is consistent with the conclusion reached.