Sample Quantiles for Ordinal Data

13 Pages Posted: 2 Sep 2018

See all articles by Uwe Hassler

Uwe Hassler

Goethe University Frankfurt - Faculty of Economics and Business Administration

Date Written: August 24, 2018


Computing the arithmetic mean over ordinal data is not a meaningful procedure. Instead it is often recommended to compute the sample median, or more generally sample quantiles. The virtue of raw quantiles is that they are not affected by an arbitrary rescaling of the data. Unfortunately, they are not very informative when an ordinal variable falls into only few categories. The informational content is larger for so-called grouped quantiles interpolating around one possible value. In this note we show, however, that they turn out to be not invariant with respect to strictly monotonous transformations as long as the possible outcomes are not equidistant. This motivates to suggest the new centered interpolated quantiles. They are designed to be invariant with respect to transformations that preserve the ranking of the possible values.

Keywords: Likert Response Format, Interpolated Quantiles, Invariance Under Strictly Monotonous Transformations

JEL Classification: C19, C29, C80

Suggested Citation

Hassler, Uwe, Sample Quantiles for Ordinal Data (August 24, 2018). Available at SSRN: or

Uwe Hassler (Contact Author)

Goethe University Frankfurt - Faculty of Economics and Business Administration ( email )

Theodor-W.-Adorno-Platz 4
Frankfurt am Main, D-60323

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