The benefit is linear but the distribution of people getting it is not evenly distributed around the middle of the benefit range. Therefore the average benefit is not just the mean of the min and max SS benefits.
PIA formula For an individual who first becomes eligible for old-age insurance benefits or disability insurance benefits in 2019, or who dies in 2019 before becoming eligible for benefits, his/her PIA will be the sum of: (a) 90 percent of the first $926 of his/her average indexed monthly earnings, plus (b) 32 percent of his/her average indexed monthly earnings over $926 and through $5,583, plus (c) 15 percent of his/her average indexed monthly earnings over $5,583.
Note the c is capped 11,075 US$ per month as income above that is not taxed.