# Median statistics estimates of Hubble and Newton's Constant

## TL;DR

This paper demonstrates the robustness of median statistics through toy experiments and applies it to estimate the Hubble Constant and Newton's Gravitational Constant, revealing significant measurement discrepancies.

## Contribution

It introduces median statistics as a robust method for estimating fundamental constants, updating previous analyses with a larger dataset and providing new median estimates.

## Key findings

- Median estimate of Hubble Constant: 72.5 km/sec/Mpc with 95% confidence interval.
- Median estimate of Newton's G: 6.674702 × 10^{-11} N m^2 kg^{-2} with 68% confidence.
- Median statistics show robustness against assumptions and measurement variations.

## Abstract

Robustness of any statistics depends upon the number of assumptions it makes about the measured data. We point out the advantages of median statistics using toy numerical experiments and demonstrate its robustness, when the number of assumptions we can make about the data are limited. We then apply the median statistics technique to obtain estimates of two constants of nature, Hubble Constant ($H_0$) and Newton's Gravitational Constant($G$), both of which show significant differences between different measurements. For $H_0$, we update the analysis done by Chen and Ratra (2011) and Gott et al. (2001) using $576$ measurements. We find after grouping the different results according to their primary type of measurement, the median estimates are given by $H_0=72.5^{+2.5}_{-8}$ km/sec/Mpc with errors corresponding to 95% c.l. (2$\sigma$) and $G=6.674702^{+0.0014}_{-0.0009} \times 10^{-11} \mathrm{N m^{2}kg^{-2}}$ corresponding to 68% c.l. (1$\sigma$).