Indonesian grade 11 students’ conceptual difficulties with measures of central tendency: An nvivo-assisted qualitative study of representativeness, visualization, and decision making
DOI:
https://doi.org/10.58524/jasme.v6i1.1072Keywords:
Measures of central tendency, Conceptual difficulties, Data visualization, Statistical reasoning, Qualitative case studyAbstract
Background: Conceptual understanding is essential in statistics learning, especially measures of central tendency, because it supports students’ ability to represent, interpret, and make data-based decisions.
Aims: This study identifies patterns of students’ conceptual difficulties in measures of central tendency across basic concepts, data visualization, data interpretation, and decision making.
Methods: A qualitative descriptive case study involved 33 eleventh-grade students from a public senior high school. Data came from a written test and semi-structured interviews with six purposively selected students. Responses were analyzed using NVivo-assisted inductive open coding. Trustworthiness was supported through data-source triangulation, peer debriefing, and an audit trail.
Result: Twenty-two initial codes were synthesized into four themes: understanding basic concepts, data visualization, data interpretation, and Application and decision making. Difficulties were most prominent in viewing central tendency as a representative value, constructing histograms and line plots, and justifying contextual decisions. Common misconceptions included computing the mean as “total frequency ÷ number of categories” and treating histogram tasks as table rewriting rather than graph construction. Overall, the pattern suggests a plausible progression linking conceptual understanding with representational and interpretive demands.
Conclusion: Students’ difficulties are interrelated and conceptually driven; instruction should emphasize representativeness, multiple representations, and evidence-based reasoning.
References
Ahmad, M., & Wilkins, S. (2025). Purposive sampling in qualitative research: A framework for the entire journey. Quality & Quantity, 59(2), 1461–1479. https://doi.org/10.1007/s11135-024-02022-5
Akar, N., & Işıksal Bostan, M. (2025). Nurturing preservice mathematics teachers’ reasoning about measures of central tendency and variability. The Journal of Experimental Education, 93(3), 478–501. https://doi.org/10.1080/00220973.2024.2349213
Allsop, D. B., Chelladurai, J. M., Kimball, E. R., Marks, L. D., & Hendricks, J. J. (2022). Qualitative methods with NVivo software: A practical guide for analyzing qualitative data. Psych, 4(2), 142–159. https://doi.org/10.3390/psych4020013
Aydın, K. Ş., & Ay, Z. S. (2025). Investigation of eighth grade students’ performance on tasks involving statistical thinking about measures of central tendency. Participatory Educational Research, 12(1), 18–42. https://doi.org/10.17275/per.25.2.12.1
Ayeh, I. G. (2025). Students’ mathematics conceptual challenges: Exploring students’ thinking, understanding, and misconceptions in functions and graphs. European Journal of Science and Mathematics Education, 13(3), 191–206. https://doi.org/10.30935/scimath/16596
Barumbun, M., & Kharisma, D. (2022). Procedural knowledge or conceptual knowledge? Developing the so-called proceptual knowledge in mathematics learning. Beta: Jurnal Tadris Matematika, 15(2), 167–180. https://doi.org/10.20414/betajtm.v15i2.472
Binali, T., Chang, C.-H., Chang, Y.-J., & Chang, H.-Y. (2024). High school and college students’ graph-interpretation competence in scientific and daily contexts of data visualization. Science & Education, 33(3), 763–785. https://doi.org/10.1007/s11191-022-00406-3
Boels, L., Bakker, A., Van Dooren, W., & Drijvers, P. (2025). Secondary school students’ strategies when interpreting histograms and case-value plots: An eye-tracking study. Educational Studies in Mathematics, 118(3), 479–503. https://doi.org/10.1007/s10649-024-10351-3
Cazorla, I. M., Utsumi, M. C., & Magina, S. M. (2023). The conceptual field of measures of central tendency: A first approximation. International Electronic Journal of Mathematics Education, 18(4), em0748. https://doi.org/10.29333/iejme/13571
De Zeeuw, A., Craig, T., & You, H. S. (2013). Assessing conceptual understanding in mathematics. In Proceedings of the IEEE Frontiers in Education Conference (FIE), 1742–1744. https://doi.org/10.1109/FIE.2013.6685135
Edelsbrunner, P. A., Malone, S., Hofer, S. I., Küchemann, S., Kuhn, J., Schmid, R., Altmeyer, K., Brünken, R., & Lichtenberger, A. (2023). The relation of representational competence and conceptual knowledge in female and male undergraduates. International Journal of STEM Education, 10(1), 44. https://doi.org/10.1186/s40594-023-00435-6
Fielding, J., & Makar, K. (2022). Challenging conceptual understanding in a complex system: Supporting young students to address extended mathematical inquiry problems. Instructional Science, 50(1), 35–61. https://doi.org/10.1007/s11251-021-09564-3
Franconeri, S. L., Padilla, L. M., Shah, P., Zacks, J. M., & Hullman, J. (2021). The science of visual data communication: What works. Psychological Science in the Public Interest, 22(3), 110–161. https://doi.org/10.1177/15291006211051956
Greeves, S., & Oz, M. (2024). YouTube in higher education: Comparing student and instructor perceptions and practices. Frontiers in Education, 8. https://doi.org/10.3389/feduc.2023.1330405
Groth, R. E., & Choi, Y. (2023). A method for assessing students’ interpretations of contextualized data. Educational Studies in Mathematics, 114(1), 17–34. https://doi.org/10.1007/s10649-023-10234-z
Gunadi, F., Herman, T., & Prabawanto, S. (2022). Students’ learning obstacle in solving statistical reasoning problems: Epistemological study. Gema Wiralodra, 13(1), 285–294. https://doi.org/10.31943/gemawiralodra.v13i1.213
Ismail, N. Z.-I., Abu Kassim, N. L., & Mahmud, Z. (2022). Factors influencing students’ understanding of basic statistical concepts. IIUM Journal of Educational Studies, 10(2), 174–204. https://doi.org/10.31436/ijes.v10i2.459
Jäder, J., & Johansson, H. (2025). Exploring students’ conceptual understanding through mathematical problem solving: Students’ use of and shift between different representations of rational numbers. Research in Mathematics Education, 1–18. https://doi.org/10.1080/14794802.2025.2456840
Kelle, U., & Buchholtz, N. (2015). The Combination of Qualitative and Quantitative Research Methods in Mathematics Education: A “Mixed Methods” Study on the Development of the Professional Knowledge of Teachers. In A. Bikner-Ahsbahs, C. Knipping, & N. Presmeg (Eds.), Approaches to Qualitative Research in Mathematics Education (pp. 321–361). Springer, Dordrecht. https://doi.org/10.1007/978-94-017-9181-6_12
Kurnia, A. B., Lowrie, T., & Patahuddin, S. M. (2024). The development of high school students’ statistical literacy across grade level. Mathematics Education Research Journal, 36(S1), 7–35. https://doi.org/10.1007/s13394-023-00449-x
Landtblom, K. (2023). Opportunities to learn mean, median, and mode afforded by textbook tasks. Statistics Education Research Journal, 22(3). https://doi.org/https://doi.org/10.52041/serj.v22i3.655
Landtblom, K., & Sumpter, L. (2025). Which measure of central tendency is most useful? Grade 6 students’ expressed statistical literacy. Statistics Education Research Journal, 24(2), 4. https://doi.org/10.52041/serj.v24i2.811
Lemieux, C., & Chapman, O. (2025). Postsecondary students’ understanding of statistics through story-based tasks. International Journal of Mathematical Education in Science and Technology, 56(9), 1725–1747. https://doi.org/10.1080/0020739X.2024.2353895
Li, F., & Wang, L. (2024). A study on textbook use and its effects on students’ academic performance. Disciplinary and Interdisciplinary Science Education Research, 6(1), 4. https://doi.org/10.1186/s43031-023-00094-1
Lian, L. H., Yew, W. T., & Meng, C. C. (2022). Assessing Lower Secondary School Students’ Common Errors in Statistics. Pertanika Journal of Social Sciences and Humanities, 30(3), 1427–1450. https://doi.org/10.47836/pjssh.30.3.26
Mahfudhoh, M., & Kurniasari, I. (2025). Concept understanding of VIIIth grade junior high school students on statistics based on APOS theory in terms of mathematical ability. AIP Conference Proceedings, 3316(1). https://doi.org/10.1063/5.0290724
Maryati, I., & Priatna, N. (2018). Analysis of statistical misconception in terms of statistical reasoning. Journal of Physics: Conference Series, 1013. https://doi.org/10.1088/1742-6596/1013/1/012206
Meydan, C. H., & Akkaş, H. (2024). The role of triangulation in qualitative research: Converging perspectives. In Principles of Conducting Qualitative Research in Multicultural Settings (pp. 98–129). IGI Global. https://doi.org/10.4018/979-8-3693-3306-8.ch006
Mokros, J., & Russell, S. J. (1995). Children’s concepts of average and representativeness. Journal for Research in Mathematics Education, 26(1), 20–39. https://doi.org/10.5951/jresematheduc.26.1.0020
Mulligan, J., Tytler, R., Prain, V., & Kirk, M. (2024). Implementing a pedagogical cycle to support data modelling and statistical reasoning in years 1 and 2 through the Interdisciplinary Mathematics and Science (IMS) project. Mathematics Education Research Journal, 36(S1), 37–66. https://doi.org/10.1007/s13394-023-00454-0
Niki, M. (2024). Does the reduction in instruction time affect student achievement and motivation? Evidence from Japan. Japan and the World Economy, 70, 101254. https://doi.org/10.1016/j.japwor.2024.101254
Ograjenšek, I., & Gal, I. (2016). Enhancing Statistics Education by Including Qualitative Research. International Statistical Review, 84(2), 165–178. https://doi.org/10.1111/insr.12158
Pozdniakov, S., Martinez-Maldonado, R., Tsai, Y.-S., Echeverria, V., Swiecki, Z., & Gašević, D. (2024). Investigating the Effect of Visualization Literacy and Guidance on Teachers’ Dashboard Interpretation. Journal of Learning Analytics, 12(1), 367–390. https://doi.org/10.18608/jla.2024.8471
Rao, A. L., Santhikumar, R., & Venugopal, K. (2025). Visualizing Insight Enhancing Statistical Thinking in Higher Education. In Modes of Representation in Developing Statistical Thinking in Education (pp. 181–214). IGI Global. https://doi.org/10.4018/979-8-3693-9934-7.ch010
Rittle-Johnson, B., & Siegler, R. S. (2021). The relation between conceptual and procedural knowledge in learning mathematics: A review. In The Development of Mathematical Skills (pp. 75–110). Psychology Press. https://doi.org/10.4324/9781315784755-6
Rosidah, R., & Ikram, F. Z. (2021). Measure of Central Tendency: Undergraduate Students’ Error in Decision-Making Perspective. International Journal of Education, 14(1), 39–47. https://doi.org/10.17509/ije.v14i1.29408
Saidi, S. S., & Siew, N. M. (2022). Assessing secondary school students’ statistical reasoning, attitude towards statistics, and statistics anxiety. Statistics Education Research Journal, 21(1), 6. https://doi.org/10.52041/serj.v21i1.67
Saputri, L. J., Susanti, N., & Dani, R. (2025). Qualitative study of NVivo-based concept understanding in lesson study learning in climate change courses. DIDAKTIKA : Jurnal Pemikiran Pendidikan, 31(1). https://doi.org/10.30587/didaktika.v31i1.9546
Sasidharan, S., & Kareem, J. (2023). Student Perceptions and Experiences in Mathematics Classrooms: A Thematic Analysis. International Journal of Innovation in Science and Mathematics Education, 31(2). https://doi.org/10.30722/IJISME.31.02.004
Schoenherr, J., Strohmaier, A. R., & Schukajlow, S. (2024). Learning with visualizations helps: A meta-analysis of visualization interventions in mathematics education. Educational Research Review, 45, 100639. https://doi.org/10.1016/j.edurev.2024.100639
Schuchardt, A. M., & Schunn, C. D. (2016). Modeling Scientific Processes With Mathematics Equations Enhances Student Qualitative Conceptual Understanding and Quantitative Problem Solving. Science Education, 100(2), 290–320. https://doi.org/10.1002/sce.21198
Star, J. R. (2005). Research Commentary Reconceptualizing Procedural Knowledge. Journal for Research in Mathematics Education, 36(5), 404–411. http://www.jstor.org/stable/30034943
Subali, B., Ellianawati, Negoro, R. A., Dwijananti, P., Anandita, A. S., & Setyaningsih, N. E. (2025). Assessing Students’ Graph Interpretation Ability Through the Use of Educational Research Statistics Learning Material. Journal of Physics: Conference Series, 3148(1). https://doi.org/10.1088/1742-6596/3148/1/012009
Svensson, C., & Holmqvist, M. (2021). Pre-Service Teachers’ Procedural and Conceptual Understanding of Pupils’ Mean Value Knowledge in Grade 6. International Electronic Journal of Mathematics Education, 16(3), em0649. https://doi.org/10.29333/iejme/11067
Thomaneck, A., Vollstedt, M., & Schindler, M. (2025). Students’ approaches when capturing change in contextual graphs: a study combining eye tracking and stimulated recall interviews. Mathematics Education Research Journal, 37(4), 889–913. https://doi.org/10.1007/s13394-025-00517-4
Xiong, X. (2025). Influence of teaching styles of higher education teachers on students‘ engagement in learning: The mediating role of learning motivation. Education for Chemical Engineers, 51, 87–102. https://doi.org/10.1016/j.ece.2025.02.005
Zentgraf, K., & Prediger, S. (2024). Demands and scaffolds for explaining the connection of multiple representations: Revisiting the bottle-filling task. Journal of Mathematical Behavior, 73. https://doi.org/10.1016/j.jmathb.2023.101118
Zin, S. H. H. B. M., Nor, R. B. C. M., & Zakaria, S. H. B. (2023). Students’ attitudes and perception towards statistics assessing students’ attitudes and perception towards statistics subject. International Journal of Service Management and Sustainability, 2(8), 17–42. https://doi.org/10.24191/ijsms.v8i2.24184
Downloads
Published
Issue
Section
License
Copyright (c) 2026 Puput Indriyani Nur haeni, Mohamad Gilar Jatisunda
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
