Student perceptions of variation in a real world context

Variation is a key concept in the study of statistics and the understanding of variation is a crucial aspect of most statistically related tasks. To express this understanding students need to be able to describe variation. Students aged 13 to 17 engaged in an inference task set in a real world context that necessitated the description of both rainfall and temperature data. This research qualitatively analysed the student responses with respect to the descriptions of variation that were incorporated. A Data Description hierarchy, previously developed for describing variation in a sampling task, was found to be appropriate to code the better responses and was extended to accommodate a range of less statistically sophisticated responses identified. The SOLO Taxonomy was used as a framework for the hierarchy. Two cycles of U-M-R levels, one for more qualitatively descriptions and the other for more quantitative descriptions, were identified in the responses. Task and implementation issues that may have affected the descriptions, as well as implications for research, teaching and assessment, are outlined.