Data analysis to explore the sampling distribution of the sample mean

Statement of the problem. Students who take elementary statistics as required for many college majors often exhibit misconceptions and inaccuracies about statistical concepts and procedures. This constructivist study was based on the theory that students build frameworks for making sense of information (Schoenfeld, 1987b).;Results. Students competently used the TI-82 to construct histograms of sample data and label the pencil copy appropriately. However, students manifested difficulty with reading histograms and interpreting them. They made inappropriate use of statistics terminology. They were unable to use a histogram of a sample to make inferences to the population.;The exercise of sampling from an unknown population to make some determination about the population was productive in assisting students to develop the concept of randomness. Nevertheless, subsequent assignments revealed that the development was limited and did not readily attach itself to new sampling situations.;For some students, the assignment of simulating the sampling distribution of the sample mean provided compelling visual evidence of the tenets of the Central Limit Theorem. For others, in spite of the attention given to developing experience with and insight into data analysis and random numbers, the outcome was not successful.;Methods. The research was a responsive evaluation (Guba & Lincoln, 1989) of college students in the context of an elementary statistics class. Data were collected on the effects of students' operational and conceptual understanding of data distributions and random sampling on their understanding of the sampling distribution of the sample mean. Students created, read, analyzed, discussed, and wrote about histograms. They selected samples from an unknown population to infer about the population. They used a computer program for the TI-82 graphing calculator (Fetta, 1994) for a project in which they drew samples from uniform, exponential, and normal populations and wrote about the activity. Interviews with four students were videotaped.;Conclusions. The research suggested that students need more experience with data analysis as a vehicle for exploring data distributions and enhancing statistics vocabulary and definitions. Students also need to develop a concept of random sampling to support inferential statistics, as constructivist theory suggests. The concept of the sampling distribution of the sample means is just another theorem to the student who does not have conceptual understanding of data analysis and sampling.