Airborne PM$_{10}$ concentration in a residential area is monitored for 24 hours by a respirable dust sampler. Initial and final weights of the filter paper are 2.3125 g and 2.6996 g respectively. The average airflow rate during sampling is 1.2 m$^3$/min. The PM$_{10}$ concentration of the area in $\mu g \, \text{m}^{-3}$ is ______.