  In order to investigate the potential Hubble tension, we compile a catalogue
of 216 measurements of the Hubble--Lema\^itre constant $H_0$ between 2012 and
2022, which includes 109 model-independent measurements and 107 $\Lambda$CDM
model-based measurements. Statistical analyses of these measurements show that
the deviations of the results with respect to the average $H_0$ are far larger
than expected from their error bars if they follow a Gaussian distribution. We
find that $x\sigma $ deviation is indeed equivalent in a Gaussian distribution
to $x_{\rm eq}\sigma$ deviation in the frequency of values, where $x_{\rm
eq}=0.72x^{0.88}$. Hence, a tension of 5$\sigma$, estimated between the
Cepheid-calibrated type Ia supernovae and cosmic microwave background (CMB)
data, is indeed a 3$\sigma$ tension in equivalent terms of a Gaussian
distribution of frequencies. However, this recalibration should be independent
of the data whose tension we want to test. If we adopt the previous analysis of
data of 1976-2019, the equivalent tension is reduced to $2.25\sigma$.
Covariance terms due to correlations of measurements do not significantly
change the results. Nonetheless, the separation of the data into two blocks
with $H_0<71$ and $H_0\ge 71$ km s$^{-1}$ Mpc$^{-1}$ finds compatibility with a
Gaussian distribution for each of them without removing any outlier. These
statistical results indicate that the underestimation of error bars for $H_0$
remains prevalent over the past decade, dominated by systematic errors in the
methodologies of CMB and local distance ladder analyses.

Cosmology and Nongalactic Astrophysics