If you have any concerns regarding the analyses, please feel free to request the output files. If a grouped median was calculated, it would certainly be present in the results.

Furthermore, percentiles such as Q1 and Q3 are not always the focus of interpretation in ordinal or grouped data, as they are generally considered secondary summary measures compared to the median. This may explain why interpolated versions were not calculated or reported in this case.

In standard statistical software such as SPSS, Q1 and Q3 are often calculated using the “discrete method” based on positional values in ordered data, rather than using grouped or interpolated estimates. This often results in Q1 and Q3 values being integers or ending in .5.

The likely reason Q1 and Q3 appear as whole numbers or end in .5 while Q2 (the median) has a fractional component is due to the computation method.

Rosner, B. (2015). Fundamentals of Biostatistics (8th ed., pp. 55–56). Cengage Learning.

Gravetter, F. J., & Wallnau, L. B. (2016). Statistics for the Behavioral Sciences (10th ed., pp. 78–80). Pearson.

Gupta, S. C. (2014). Fundamentals of Statistics (7th ed.). Himalaya Publishing.

This method is widely supported in statistical literature and is implemented in standard statistical software packages, including SPSS. Several authoritative sources explain both the rationale and the procedure for grouped median computation:

In grouped data, the median is not simply the middle score but an estimated value derived from cumulative frequencies within a defined class interval. This process leads to fractional results, especially when the data are skewed or asymmetrically distributed.

Yes, grouped median values can indeed have decimal (fractional) components, and this is a natural result of the interpolation method used in their calculation.

We frequently encounter such situations in our analyses and often report grouped median values. It is highly likely that the researcher in this case followed the same approach to enhance interpretability.

Otherwise, even if the medians are the same, differences in distribution might exist, requiring additional analyses such as distribution width, mode, or interquartile range to explain the findings accurately.

Grouped median highlights the class in which the data are most concentrated, providing a central tendency measure based not only on position but also on frequency. This approach supports clearer interpretation, especially with limited-scale response formats.

This inconsistency makes interpretation difficult for researchers. In such cases, using the grouped median offers a more informative summary of the data and better represents the concentration of responses across the scale.

This limitation may lead to situations where the p-value shows statistical significance between two groups, yet the median values remain the same. In such cases, a perceived inconsistency emerges between statistical significance and the measure of central tendency.

Likert-type data, due to their ordinal nature, can present challenges in the use of the median as a measure of central tendency. Since these data do not include decimal values, the median often falls within a limited range—typically 0 or 0.5.