Senior high school students’ poor performance, errors and misconceptions in determining measures, of variation in statistics

Abstract

This study examines Senior High School students' errors and misconceptions in understanding statistical measures of variation, focusing on students at Winneba Senior High School, Ghana. Statistics, a critical discipline for data interpretation and informed decision-making, often presents conceptual and procedural challenges, particularly regarding measures such as range, variance, and standard deviation. The research employed a mixed-methods approach within a pragmatist paradigm, utilising an exploratory sequential design. Quantitative data were collected through structured assessments administered to 140 final-year students to identify their errors and misconceptions in dealing with tasks on measures of variation. Subsequently, semistructured interviews with a purposively selected subset of 10 students provided qualitative insights into their reasoning and cognitive challenges. The findings revealed that students frequently confuse measures of central tendency with variation, misuse statistical formulas, and struggle with abstract concepts like deviation and distribution. Common errors included conflating range and standard deviation, misinterpreting variability, and relying heavily on rote memorisation of formulas without understanding their applications. Pedagogical approaches emphasizing procedural skills over conceptual understanding, insufficient use of real-world data, and linguistic barriers in statistical terminology were identified as key contributors to these challenges. The study concluded that traditional teaching methods inadequately address the cognitive demands of statistical reasoning. It recommended integrating experiential learning strategies, real-world data applications, and enhanced teacher training programs focused on fostering statistical reasoning and interpretation.