Interpreting statistics teachers page

Secondary activities
Secondary StatZing! March 2004 Interpreting statistics activity

Curriculum links

NCEA Mathematics Achievement Standard 1.5 (AS 90913):

• Use straightforward methods to explore data.
  The activity is a suitable teaching resource, not an assessment for this standard.

• Interpret statistical information and comment on a range of features.

Background
The activities in StatZing! use data collected from the CensusAtSchool survey. The survey was conducted in August and September 2003 and 18,000 students took part. The activities are based on samples randomly selected from the large mulitivariate dataset.

Years 9 and 10 student heights: Students complete a series of questions based on the data and the box and whisker graph.

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.

Favourite subject at school: Students complete a series of questions and construct a bar graph using selected data for Years 9 and 10 students and Years 5 and 6 students.

StatZing! - Interpreting statistics. Suggested answers:

Years 9 and 10 student heights - paired box and whisker graphs

1. 100.
2. Scale in tens.
3. Year 10 = top graph, Year 9 = lower graph.
4. Year 9: range = 70, minimum = 130.
   Year 10: median = 168, maximum = 187 (or close to).
5. Approx 50%. Approx because we do not know how many readings, if any, are 163cms.
6. Those in the sample of Year 10 students, with a median height of 168cm, are taller on average than the Year 9 students, who have a median height of 163cm.
7. The two data sets have a similar spread with a range of 70cm for Year 9s compared with a range of 67cms for Year 10s. The interquartile ranges are also similar.
8. 25% or similar.
9. The range, mean, and maximum would decrease but the median would remain similar.
10. Similarities: averages (median, mean), would not change much.
    Differences: extreme values (minimum, maximum) and range may change considerably, due to possible outliers.
11. Limitations:
    • self-selected schools so data is not necessarily representative
    • students may fill in survey unsupervised and may give inaccurate data
    • sample size is not very big.
    Further information:
    • take a random survey within your own school
    • take international CensusAtSchool data – analyse data sets from different schools and or countries.
      
      

Favourite Subject at School – comparing years 5 and 6, years 9 and 10 students

1. Categorical.
2. Bar graph (to be drawn).
3. Years 9 and 10 Physical Education, Years 5 and 6 Art.
4. False (At Years 9 and 10, 8% of boys and 18% of girls prefer Art ; while at Years 5 and 6, 41% of girls and 29% of boys prefer Art).
5. Similarities: PE is popular with a higher percentage of boys than girls for both groups; Dance or Drama ranks in the top three subjects for girls for both groups (or similar).
6. Differences: For Years 5 and 6 Art is most popular, while for Years 9 and 10 PE is the most popular overall. Maths is second most popular for Years 5 and 6 boys but 5th favourite with Years 9 and 10 boys.
7. Limitations:
   • sample size
   • some subject names are not common to both groups.
   Improvements:
   • separate the year groups
   • combine boys and girls
   • have larger samples
   • include other variables such as age.

Related links
CensusAtSchool Project