Multi- variate data

1. Multi-variate data 90135 internal 4 Credits

2. achieved • The student: • Poses an appropriate comparison question, with or without guidance from the teacher, or is given a question to work with by the teacher. • Draws graph(s) that allow features of the data to be described in relation to the question. • Writes statements that describe comparative features of the distributions in context. (At least two statements, describing different features, are expected.) • Makes an informal inference about the population from the sample data OR answers the comparison question

3. merit • The student: • Poses an appropriate comparison question with or without guidance from the teacher. • Draws graph(s) and gives summary statistics that allow features of the data to be described in relation to the question. • Writes statements with evidence that describe comparative features of the distributions in context. (At least two statements, describing different features are expected.) • Makes an informal inference about the population from the sample data AND answers the comparison question. Gives at least one statement of supporting evidence.

4. excellence • The student: • Poses an appropriate comparison question without guidance from the teacher. • Draws graphs and gives summary statistics that allow features of the data to be described in relation to the question. (At least two different graphs showing different features are expected.) • Writes statements with evidence that describe key comparative features of the distributions in context. (At least three statements describing different features are expected, key features include middle 50%, shift and overlap, and at least two of shape, spread, unusual or interesting features.) • Makes an informal inference about the population from the sample data that shows an understanding of sampling variability and of the context. • The comparison question is answered with reference to the population and key supporting evidence summarised in context. (What the statistical basis for the claim is, and the effect of sampling variability or does the claim make sense considering the actual situation

5. Data set • S:\Maths\NCEA\Level 1\draft new standards for 2011\internal\91035 multivariate data\data set.docx

6. Achieved example • Does the time taken to get to school by bus tend to be longer than the time taken to walk to school for year 11 students in the CensusAtSchool database?

7. Data listed

8. Analysis • Achieved • (Using the dot plot only). The bus times are clustered around 20-30mins whereas the walk times are clustered around 10-20mins. The overall spread of the bus times to school is greater than the overall spread of the walk times to school. • Merit( summary statistics are given) • (Using the box plot only). The middle 50% of times to school by bus (20-40mins) are slightly more spread than the middle 50% of times to school by walking (8-23mins). The median for times to school by bus (30 mins) is a lot higher than the median for times to school by walking (17 mins) and both medians are outside the overlap of the boxes.

9. analysis • Excellence (more than one graph drawn and summary statistics given) • The times to school by bus have a peak around 20-30 minutes and are skewed to the right. The times to school by walking peak around 20 minutes and are skewed to the right as well. • The middle 50% of times to school by bus are from 20 to 40 minutes which are further up the scale (higher) than the middle 50% of times to school by walking which are 8 to 23 minutes. • The median time to school by bus is 30 minutes which is 13 minutes higher than the median time to school by walking (17 minutes). Both the medians are outside the overlap of the two boxes. • The bus times have spikes at 20 and 30 minutes and I think this may be due students rounding their times to the nearest ten minutes.

10. Conclusion/inference • Achieved: The times by bus tend to be greater than the times for walking than Year 11 students • Merit: I would claim that the times to school by bus tend to be greater than the times to school by walking for year 11 students in the CensusAtSchool database. I would make this claim as the medians are both outside the overlap of the boxes.

11. conclusions • Excellence: I would claim that the times to school by bus tend to be greater than the times to school by walking for year 11 students in the CensusAtSchool database. • My claim is based on the evidence present in the sample. The middle 50% of times to school by bus are further up the scale than the middle 50% of times to school by walking and both medians are outside the overlap of the boxes. This suggests that what I see here in the samples would also hold back in the Census At School database for year 11 students. • If I was to repeat this sampling process I would expect to see this pattern persist as the distance between the medians is large enough compared to the overall visual spread, that is, that times to school by bus tend to be greater than times to school by walking for year 11 students. • From my general knowledge the claim makes sense to me because people who take the bus to school tend live a lot further away than those who walk. Those who walk tend to live within a reasonable distance for walking and therefore take a shorter time to get to school