Parton distribution functions (PDFs) play a central role in calculations for the LHC. To gain a deeper
understanding of the emergence and interplay of constraints on the PDFs in the global QCD analyses, it is
important to examine the relative significance and mutual compatibility of the experimental datasets
included in the PDF fits. Toward this goal, we discuss the L2 sensitivity, a convenient statistical indicator
for exploring the statistical pulls of individual datasets on the best-fit PDFs and identifying tensions
between competing datasets. Unlike the Lagrange multiplier method, the L2 sensitivity can be quickly
computed for a range of PDFs and momentum fractions using the published Hessian error sets. We employ
the L2 sensitivity as a common metric to study the relative importance of datasets in the recent ATLAS,
CTEQ-TEA, MSHT, and reduced PDF4LHC21 PDF analyses at next-to-next-to-leading-order and
approximate next-to-next-to-next-to-leading-order. We illustrate how this method can aid the users of
PDFs to identify datasets that are important for a PDF at a given kinematic point, to study quark flavor
composition and other detailed features of the PDFs, and to compare the data pulls on the PDFs for various
perturbative orders and functional forms. We also address the feasibility of computing the sensitivities
using Monte Carlo error PDFs. Together with the article, we present a companion interactive website with a
large collection of plotted L2 sensitivities for eight recent PDF releases and a C++ program to plot the L2
sensitivities
