We show that for any compact convex body Q in the plane, the average distance from the Fermat-Weber center of Q to the points in Q is at most $\frac{99-50\sqrt{3}}{36}\cdot \mathrm{\Delta }(Q)<0.3444\cdot \mathrm{\Delta }(Q)$, where $\mathrm{\Delta }(Q)$ denotes the diameter of Q. This improves upon the previous bound of $\frac{2(4-\sqrt{3})}{13}\cdot \mathrm{\Delta }(Q)<0.3490\cdot \mathrm{\Delta }(Q)$. The average distance from the Fermat-Weber center of Q is calculated by comparing it with that of a circular sector of radius $\mathrm{\Delta }(Q)/2$, whose area is the same as that of Q. As compared to the points of that circular sector, the distances of some points of Q to the considered Fermat-Weber center are larger. A method for evaluating the average of all varied distances is given.

我们表明，任何紧凸体Q在飞机上，从费马-韦伯中心的平均距离Q的点Q最多$\frac{99-50\sqrt{3}}{36}\cdot \mathrm{\Delta }（问）<0.3444\cdot \mathrm{\Delta }（问）$， 在哪里 $\mathrm{\Delta }（问）$表示Q的直径。这改善了之前的限制$\frac{\mathrm{2个}（4-\sqrt{3}）}{13}\cdot \mathrm{\Delta }（问）<0.3490\cdot \mathrm{\Delta }（问）$。距费马-韦伯Q中心的平均距离是通过将其与半径为圆形的扇形的平均距离进行比较来计算的$\mathrm{\Delta }（问）/\mathrm{2个}$，其面积与Q相同。与该圆形扇区的点相比，Q的某些点到考虑的Fermat-Weber中心的距离更大。给出了一种用于评估所有变化距离的平均值的方法。